The Coase Theorem is very likely the most famous and the most thoroughly analyzed proposition associated with contemporary law and economics.⁽¹⁾ The Theorem, however, was not formalized by Coase; indeed, as is well known, Coase's informally stated argument was labelled a theorem by George Stigler, not by Coase himself. Significant efforts to formalize the Theorem have been made by, among others, Stigler himself, Donald Regan, and Herbert Hovenkamp.⁽²⁾ This Article presents another approach to understanding the basic counterintuitive logic of Coase's original argument. Instead of stating Coase's argument as a proposition in neoclassical economics (like Stigler), or as a statement or statements about legal rules (like Regan and Hovenkamp), this Article's approach is to translate the essential logic of the argument into a proposition in game theory. In so doing, the counterintuitive quality of Coase's logic can be captured in a way that escapes alternative methods of abstracting his stories of ranchers, farmers, confectioners, and doctors, among others. This logic, I will suggest, supports legal regulation that counters undesirable threat bargaining.⁽³⁾

In game-theoretic terms, the logic that generates the Coase Theorem can be stated succinctly. The basic Coasean point, this Article will contend, is that the given payoff numbers in a matrix⁽⁴⁾ are not immutable. Put another way, the central theme of this Article is the identity between the logic of the Coase Theorem and the logic of payoff indeterminacy. Unless dealings are precluded, parties can bargain to increase one party's payoff and correspondingly reduce the payoff of the other party. Payoffs are thus indeterminate--"up for grabs."⁽⁵⁾ This premise has significant consequences for game-theoretic analysis. When viewed from a Coasean perspective, many matrices that lack analytical interest in standard terms become rich loci of promise and threat-strategies for the players.⁽⁶⁾

A major value in translating Coasean logic into game-theoretic terms is that it facilitates logical analysis of situations in which transaction costs are not zero. Though Coase has always insisted on the centrality of such analysis,⁽⁷⁾ logical analysis of Coasean stories (beginning with Coase himself) has instead focused on the counterfactual situation in which transaction costs are nonexistent.⁽⁸⁾ But this Article will focus on the logic of non-zero transaction cost cases.

In Part II, I will describe the payoff matrix representing Coasean bargaining in which one player promises to play her nonpreferred strategy in return for a payment from the other player.⁽⁹⁾ Part III will demonstrate the implications of a game-theoretic analysis for certain issues concerning bargaining behavior and the possibilities for income redistribution through law.⁽¹⁰⁾ Part IV introduces the analysis of a relatively unrecognized form of Coasean bargaining--threat bargaining in which one player threatens that she will play the other player's and her own nonpreferred strategy unless she receives a payment.⁽¹¹⁾ Previous consideration in the law and economics literature of strategic behavior issues associated with the Coase Theorem has focused on impediments to the parties' reaching beneficial agreements. The claim of this Article is a related, but much broader one: the logic of the Coasean story, rightly understood, demonstrates that strategic behavior is an issue in many situations in which a non-Coasean analysis fails to discern the potential for such behavior.

I will contend that Coasean logic means that the numbers of a payoff matrix are subject to side payments.⁽¹²⁾ It follows that one or both parties have an incentive to threaten the other in many matrices in which a standard game-theoretic analysis perceives no such threat possibility. Most of this Article will be devoted to analyzing threat bargaining, given the Coasean logic of payoff mutability. Part V discusses the implications of the analysis on law.⁽¹³⁾ This Article suggests that there is a "Coasean tradition" derived from, though not directly stated in, Coase's work, which opposes mandatory regulation that compels people to act in a certain way and precludes bargaining. Contrary to this tradi-

tion, this Article contends that the logic of the Coasean story,⁽¹⁴⁾ rightly understood, suggests the potential value of such regulation.⁽¹⁵⁾

Standard game-theoretic analysis takes the payoffs of the parties in a game for a given combination of strategies as unalterable.⁽¹⁶⁾ For example, if one player, Row, plays strategy ii and the other player, Column, plays strategy I, the outcome is a set of fixed payoffs for both players, such as 0 for Row and 5 for Column, which cannot be changed. The simple 2 x 1 matrix below illustrates the standard assumption:

Row

Column

(1,1)

(0,5)

Note: Row's payoffs come before Column's. In Table 1 and all other tables, a variety of numbers could be used. For ease of presentation, numbers rather than formulas have been used in the tables.

Assuming fixed payoffs, with no side payments, tends to make the analysis of strategic interaction simple in many cases. Indeed, in Table 1 that assumption makes the matrix trivially simple to analyze: Row will simply play strategy i, resulting in both players getting 1.

In many circumstances, though, the standard assumption of unalterable payoffs is highly questionable. For example, in Table 1 suppose the payoffs to the players are in dollars or some other commensurable units, and that the players are able to communicate. In that case, Column has an incentive to promise Row a payment so that Row will play ii instead of i. To be attractive to Row, the payment must be at least 1, and to be affordable by Column, it can be no more than 4. In this case, the standard analysis of the matrix, which simply says that Row will play i, is counterfactual in ruling out the possibility of a deal between the players that will increase Row's payoff for playing ii.

Against the standard game-theoretic assumption of unalterable payoffs, one can juxtapose an opposed position: payoffs are mutable and up for grabs, because the distribution of rewards for a given combination of strategies is always subject to negotiation by the players.⁽¹⁷⁾ This opposing position will be called the "Coasean position."⁽¹⁸⁾ As stated, the Coasean position acts as a reminder of the indeterminacy of the standard analysis of situations like Table 1, pointing out the possibility of the players' agreement to have Row play Column's preferred strategy in return for a payment. Stated in this form, there is nothing counterfactual about the Coasean position;⁽¹⁹⁾ it simply points out the overreaching of the standard assumption of fixed payoffs and the attendant "standard analysis."

The Coasean position means that the parties in what appears to be a 2 x 1 matrix of Table 1 (in which the choosing party will simply play the strategy that yields her the higher payoff) are actually, unless dealings between them are precluded, in a 2 x 2 matrix. In that 2 x 2 matrix, both players face the choice of whether to cooperate by reaching and adhering to an agreement under which Column pays Row in return for Row playing Column's preferred strategy.⁽²⁰⁾

The transformation of the 2 x 1 matrix in Table 1 into a 2 x 2 matrix is shown below:

Table 2
The Coasean Understanding of a Two-Person Game--
How a 2 x 1 matrix is actually a 2 x 2 matrix

Row

Column

(1,1)

(0,5)

Row

Column

(Don't Pay)
I

(Pay)
II

(1,1)

(1+x, 1-x)

(0,5)

(x, 5-x)

All of the nuisance stories involving the rancher and the farmer that Coase used to establish his argument can be expressed in game-theoretic terms.⁽²¹⁾ As games, Coase's nuisance examples all have the same basic structure. One player, Row, has a choice of strategies. One strategy, i, will yield a higher payoff for Row than another strategy, ii, but a lower payoff for the other player, Column.⁽²²⁾

For example, consider the Coasean cattle who trample the farmer's crops.⁽²³⁾ The parties' situation can be illustrated in matrices that demonstrate different possibilities as to the liability rule and as to whether protecting against trampling maximizes the total payoffs of the farmer and the rancher.⁽²⁴⁾ The key situation, shown in Table 3,⁽²⁵⁾ occurs when protection is efficient, (that is, it maximizes total payoffs) but the party who is able to provide it is not liable.⁽²⁶⁾

Assume Crop protection by ther ancher is efficient andthe rancher is not liable.

The rancher is Row and the farmer is Column; rancher's payoffs are first; payoffs include liability or compensation

No Protection

Row

Protection

Column

(1,1)

(0,5)

(NP)

Row

(P)

Column

(Don't Pay)
I

(Pay)
II

(1,1)

(1+x, 1-x)

(0,5)

(x, 5-x)

x is the amount that C pays R if agreement is reached and complied with by C; 1 < x < 4

In Table 3⁽²⁷⁾ protection is efficient but the party who can efficiently protect is not liable. Under standard game-theoretic analysis, Row will simply play the no-protection strategy, leaving Row and Column in the suboptimal (1, 1) box. Coasean logic points out the indeterminacy in this conclusion. Column has an incentive to offer Row between 1 and 4 to play the "protection" strategy, and if an agreement is in fact made and complied with, the efficient outcome will be accomplished.

The matrices in Table 2 and Table 3 are realistic because they leave open the possibility of whether an agreement will result and whether the players will comply with such an agreement. The Coasean argument can also be reformulated in a stronger, counterfactual form as an assumption that possible agreements for side payments between players will in fact be made and honored. Under this assumption, players in a game, such as those in Table 2 or 3, will choose the combination of strategies that yields the highest total payoff for them.⁽²⁸⁾ This side-payments assumption is extremely questionable in many circumstances. What if the players cannot communicate? What if performance cannot be simultaneous, and agreements are not enforceable? What if the units of the players' payoffs are difficult to measure or compare?⁽²⁹⁾ The side-payments assumption, however, allows predictions about the outcomes (though not the distribution of the payoffs) in certain situations in which the basic Coasean point (that payoffs are negotiable) does not allow such predictions.⁽³⁰⁾

Under the side-payments assumption, what matters is the sum of the players' payoffs for a given combination of strategies, rather than the distribution of that sum, which can always be altered by bargaining between the two players. The outcome in a game, such as the one shown in Table 1, is not altered if the payoffs for a given combination of strategies are increased for one player and correspondingly reduced for the other. So, for example, if the payoffs for the i, I combination in Table 1 are changed from 1, 1 to 10, -8, the outcome of the game will not vary; Row will still play ii. The distribution of payoffs may well change, because Column now will have to pay at least 5 to Row, and may pay as much as 13. But under the side-payments assumption, the combination of strategies with the highest payoff total--the efficient outcome--will be played, just as before.⁽³¹⁾

The foregoing discussion can be readily applied to legal entitlements and the liability rules associated with them. Liability rules, defined as legal rules providing for payments from one player to another (not to a third party such as the government), do not affect the sum of the two players' payoffs for a given strategy, because a reduction in one player's payoff is compensated for exactly by an increase in the other player's payoff. If the railroad is liable for spark damage to the farmer's crops, the total payoff for the railroad's emitting sparks remains the same, even though the distribution of that payoff has changed.⁽³²⁾ The same analysis also applies to property rights. Suppose the farmer has a right, enforceable by injunction, not to have the railroad emit sparks on her property. Under the side-payments assumption, this simply means that the railroad has to pay the farmer to waive her right. Once again, the total payoff of the parties for the railroad's emission of sparks is unaltered, even though the distribution of the payoff is different depending on the presence or absence of the property right. Accordingly, under the side-payments assumption, a change in liability rules or property rights will not affect the strategies that the players employ. Before or after the change, the combination of strategies that yields the highest total for the players' payoffs will be chosen by the players. Regardless of the liability rule,⁽³³⁾ the efficient outcome will result.⁽³⁴⁾

Thus, if one assumes that side payments will be made, the game-theoretic understanding of Coasean logic can be extended to generate the familiar Coase Theorem result concerning the irrelevance of legal liability and property rules to efficient outcomes. The central contribution of the game-theoretic understanding, though, lies not in confirming familiar understandings, but in detaching the logically and empirically sound assumption implicit in Coase of the mutability of payoffs from additional, questionable claims concerning whether, and under what circumstances, side payments will in fact be made. Coase's original argument focused on the side-payment issue and did not explicitly make the point that payoffs are mutable. The game-theoretic reformulation shows the difference between the correct Coasean position that standard analysis counterfactually assumes immutable payoffs and questionable assumptions about whether and when side payments will be made.

The basic Coasean position, as defined here, is that the standard game-theoretic assumption of unalterable payoffs is counterfactual, because it neglects the incentives of players to bargain for and make side payments. In this limited form, Coasean logic is unassailable. Matters become difficult regarding the side-payments assumption that available agreements will result and be honored. Coase, well recognizing the practical difficulties with this assumption, claimed only that the assumption held true under zero transaction costs. This is an assumption of extreme unrealism under which, as Coase has put it, "[T]he institutions which make up the economic system have neither substance nor purpose,"⁽³⁵⁾ and in which "eternity can be experienced in a split second."⁽³⁶⁾

A non-game-theoretic transaction-cost analysis that simply asserts, "Cooperating is less likely when many parties must coordinate" is not too useful. It would be desirable to be able to say more about whether people will enter into mutually beneficial agreements and abide by them than Coase's transaction-costs approach, or a slight modification of that approach,⁽³⁷⁾ permits. In this regard, a game-theoretic interpretation of the logic of the Coasean argument in some circumstances allows a sharper, more incisive analysis of certain issues concerning cooperation.

In many situations, a payment for cooperation involves more than a simple exchange of money for a single action; the requisite actions may well be complex and extend over a period of time. In Coasean bargaining over a surplus, whether self-interested egoists will cooperate depends on the degree to which their promises are enforceable.⁽³⁸⁾ A game-theoretic analysis demonstrates just how enforceable promises must be for cooperation to occur. For example, assume that in the basic Coasean bargaining matrix, represented in Table 4, the players agree that Row will play ii in return for a payment of 2.5 from Column. Table 4 below shows that the applicable payoff matrices, if the probability that both sides' promises will be enforced are 0, 1 or 1/2.⁽³⁹⁾

Table 4
Enforcement of Agreements in Coasean Bargaining:
Equal Division of Surplus

Assumptions: (1) R and C have agreed for R to perform C's preferred action in return for a payment of 2.5 to R; (2) the legal system awards compensatory expectation damages

(D)

Row

(C)

No Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(3.5,-1.5)

(0,5)

(2.5,2.5)

(D)

Row

(C)

100% Probability of Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(-.5,2.5)

(2.5,2.5)

(D)

Row

(C)

50% Probability of Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(1.5,.5)

(1.25,3.75)

(2.5,2.5)

For Column (the paying player) the maximizing strategy remains defecting unless there is perfect enforceability. Even in this scenario, Column has no preference for paying over reneging, given her knowledge that Row will cooperate.⁽⁴⁰⁾ On the other hand, for Row, as the performing player, the balance is in favor of complying through performance when the probability of enforcement is 1/2; therefore, as long as the probability of enforcement is over 40%, Row should cooperate.⁽⁴¹⁾ Thus, it is possible to specify how effective the legal system must be in order to make the Coase Theorem proposition (that the liability rule will not affect the efficient outcome) possibly correct⁽⁴²⁾ in a one-shot case in which the parties cannot or do not enforce compliance themselves by making the exchange of Row's performance and Column's payment simultaneous. Given the payoffs here, the proposition will not be true when the legal system enforces agreements less than 40% of the time.

B. Why Powerful Parties May Prefer a Nominally Even Agreement to a One-Sided Agreement

In addition to making it possible to analyze the effect of agreement enforceability, a game-theoretic analysis of Coasean bargaining can be brought to bear on issues of bargaining behavior which are a black box within standard interpretations of the Theorem. One such issue is how a calculating egoist with greater bargaining power than another person will press her advantage. Suppose a legal environment in which the probability of an agreement to be enforced is 1/2, and further suppose that Column, the paying player, has the ability to get Row to agree to cooperate by playing strategy ii in return for a payment of only 1.5; Column will wind up getting 3.5, the lion's share of the surplus, from cooperation. It may seem that entering into an agreement with Row paying as little as possible is an unalloyed good to Column, but a game-theoretic analysis reveals that it is not. Table 5 represents the situation, with the probability of enforcement of the agreement equal to 1/2, but with an unequal division of the surplus.

Table 5
Enforcement of Agreements in Coasean Bargaining: Unequal Division of Surplus

Assumptions: (1) R and C have agreed for R to perform C's preferred action in return for a payment of 2.5 to R; (2) the legal system awards compensatory expectation damages

(D)

Row

(C)

No Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(2.5,-.5)

(0,5)

(1.5,3.5)

(D)

Row

(C)

100% Probability of Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(-.5,2.5)

(1.5,3.5)

(D)

Row

(C)

50% Probability of Enforcement
Column

(Defect)
I

(Cooperate)
II

(1,1)

(.5,1.5)

(.75,4.25)

(1.5,3.5)

Assuming that the legal system enforces agreements 50% of the time and that this is known to both players, the rational response by the weaker party Row to the stronger party Column's defection or anticipated defection is to defect, which would leave Column with only one option: to avoid Row's defection, the best strategy for the powerful party Column is to cooperate immediately by paying upon entering into the agreement. This will cause Row to cooperate, resulting in Column and Row getting the 3.5 and the 1.5, respectively, that they had bargained for in the agreement.⁽⁴³⁾

The result is ironic because the outcome for Column, the powerful party, is worse than the outcome from the parallel situation with 50% enforceability in which the agreement between the players is for an equal division of the surplus. As demonstrated in Table 4, Column ends up getting 3.75 and Row, the weaker party, only 1.25. That is, Column's expectation in the imperfect enforcement situation is greater if she enters into a nominally even agreement to pay 2.5, from which she will subsequently defect, than if she enters into an agreement to pay only 1.5. Column obtains the best results with an agreement to pay just under 2, wherein she receives slightly less than 4 and Row gets slightly more than 1.

From the parties' viewpoint, they may bargain for both the enforceability of the agreement as well as the price. Row and Column negotiate not only about the price Column will pay Row, but also how readily enforceable their agreement will be. For the parties, Coasean bargaining is not simply a matter of agreeing on a price for an action; there is also bargaining, implicit or explicit, in their agreement about the level of enforceability.⁽⁴⁴⁾

From the standpoint of the participants within the legal system--such as attorneys, judges, and political activists--the level of enforceability of agreements may well be subject to alteration, just as it is for the parties. For example, a judge may or may not accept an unconscionability argument to allow a consumer to escape the obligations of a contract. Similarly, a legal-aid lawyer or a community activist may or may not encourage the purchaser to challenge the contract in the first place. Their choices, directly in the judge's case and indirectly in the case of other system participants, affect the degree to which the consumer Column's promise to pay will be enforceable.

Assume a participant in the legal system wishes to intervene on an egalitarian basis to favor the weaker party in a contractual transaction.⁽⁴⁵⁾ A standard law and economics rejoinder is that such intervention--through, for instance, relieving a consumer of onerous terms--is self-defeating, because the seller will either withdraw from the market or exercise her advantage in bargaining power over the consumer in some other fashion. This standard law and economics response is too sweeping. A game-theoretic analysis can be applied to show how a calibrated, variable level of enforcement of agreements can lead to an outcome in which legal intervention can benefit the weaker party.⁽⁴⁶⁾

Table 6
Enforcement of Agreements in Coasean Bargaining:
Legal Intervention on Behalf of the Weaker Party

Assumptions: (1) R (the stronger party) and C (the weaker party) have agreed for R to perform C's preferred action in return for a payment of 3.75 to R; (2) the legal system awards compensatory expectation damages); and (3) the legal system enforces the promises of weak and strong parties differentially, depending on factors such as unconscionability

(D)

Row-Stronger

(C)

Column-Weaker

(Defect)
I

(Cooperate)
II

(1,1)

(.75,1.25)

(0,5)

(3.75,1.25)

Outcome: Indeterminate; the stronger party suspects the weaker party will defect, and may well therefore defect, meaning that no bargain will be carried out.

Situation 2--The stronger party's promises are enforceable, along with a sufficient proportion of the weaker party's promises to make cooperation advantageous for the stronger party.

(D)

Row-Stronger

(C)

Column-Weaker

(Defect)
I

(Cooperate)
II

(1,1)

(.75,1.25)

(2,3)

(3.75,1.25)

Outcome: Cooperation by the stronger party, since regardless of whether the weaker party defects, cooperation yields better outcomes for the stronger party.

In the situation illustrated in the first part of Table 6, simply relieving the weaker party of its contractual obligation may harm that party by causing the transaction to become worthless, thus eliminating the incentive of the stronger party to engage in the activity at all. This is a standard law and economics argument. On the other hand, providing partial enforcement of promises by the weaker party--which may be the practical effect of open-ended standards like unconscionability--redistributes income from the stronger to the weaker party,⁽⁴⁸⁾ while still making the transaction sufficiently worthwhile for the stronger party to continue participating.⁽⁴⁹⁾

As previously noted, the Coasean position is that payoff numbers are mutable.⁽⁵⁰⁾ The numbers cannot be altered in any way that the players desire, but they can be altered through bargaining. This Coasean proposition leads to game-theoretic analyses that differ in significant respects from standard game-theoretic analyses and standard interpretations of the value of encouraging bargaining. We will now turn to these game-theoretic analyses, which are based upon the Coasean premise concerning the mutability of payoffs.

In a standard game-theoretic analysis, there is no analytical interest in a 2 x 1 matrix in which only one player alone is able to choose. That player (Column) simply chooses the option that gives her the higher payoff, with the other player (Row) playing a purely passive role. In a Coasean framework, on the other hand, 2 x 1 matrices often create opportunities for deals between the parties to circumvent the matrix's numbers. Not all such matrices have this capacity; it depends on the relationship between the parties' payoffs.

First, take the case in which Row is the choosing player, where her preferred choice is Ri and her other choice is Rii. Column's payoff when Row plays Ri is Ci; the payoff when Row plays Rii is Cii. In this situation, the standard analysis states that the outcome is simply Ri, Ci. Coasean analysis comes to radically different conclusions for most values of Ri, Rii, Ci, and Cii.

The obvious case in which Coasean logic leads to a different conclusion as to the players' payoffs is the one discussed previously in Table 2 and elsewhere,⁽⁵¹⁾ in which R and C both have incentives for C to offer a payment to R to prompt her to play C's preferred strategy, which is different from R's preferred strategy. This occurs whenever C is helped more by R's playing her unpreferred strategy than R is hurt by doing so; that is, when Cii - Ci > Ri - Rii > 0. In this case, the players can make a deal for R to pay C anywhere in the range between Ri - Rii and Cii - Ci. For example, in the matrix shown in Table 2, the players have an incentive to make a deal in which C pays R between 1 and 4 to play ii.

No effective incentives exist for a player to propose a deal if R's loss from playing her unpreferred strategy is greater than C's gain from R doing so. In other words, no deal exists when Ri - Rii > Cii - Ci > 0. Therefore, in the situation in which the payoffs are 5, 0 if rancher Row does not protect farmer Column's crops and 1, 1 if he does, the probability for deal-making to circumvent the 5, 0 outcome is minuscule. The farmer, of course, wishes that the rancher would choose to protect his crops so that he could get 1 instead of 0, but lacks the ability to offer the rancher enough to make it worth his while to do so. Thus in this case, the standard analysis and the Coasean analysis of the matrix converge in their results, with both finding no alternative to the 5, 0 outcome.

Thus far, we have focused on situations in which R's preferred choice is C's unpreferred choice. When we turn to the broad array of situations in which R's preferred choice of strategy is also C's preferred choice, we arrive at a central divergence between standard game-theoretic analysis and an analysis based on the mutability of payoffs. At first glance, it might seem that these situations represent a clear harmony between the players' interests, and offer no opportunity for the players' to deviate from the numbers of the payoff matrix. But they do offer such an opportunity, in that R has an incentive to threaten C by stating that she will play her own (and C's) unpreferred strategy unless C pays R a certain amount.⁽⁵²⁾

An example of threat bargaining that does not involve a surplus is Coase's discussion of the situation under which the rancher is liable and production is inefficient for the farmer because the value of crops is $10 but the cost of cultivation is $11.⁽⁵³⁾ This particular land is used by the cattle as a pathway, so if the farmer cultivates the pathway, it is likely that all the crops will be destroyed, resulting in a payment of $10 by the rancher to the farmer.

Like Coase's other examples, this one can be modelled as a 2 x 1 matrix.⁽⁵⁴⁾

Assumptions: (1) The rancher is liable for crop damage; and (2) Cultivating crops will cause a loss of 1 to the farmer* and a liability of 10 to the rancher.**

Grow

Row

Don't Grow

Column
I

(-1,-10)

(0,0)

* The crops are worth 10 but cost 11 to cultivate.
** The crops lie along a path trodden by cattle.

Under a standard game-theoretic analysis that assumes fixed payoffs, the farmer does not cultivate the pathway. Under a Coasean analysis, though, the result is not so readily apparent since the farmer has an incentive to seek a payment of up to $10 from the rancher⁽⁵⁵⁾ in exchange for the farmer's noncultivation.

In addition to Coase's example of a threat,⁽⁵⁶⁾ many other instances of the threat-bargaining situation involve circumstances under which a given activity is either noxious to both parties or beneficial to both. For example, suppose a factory owner is considering whether to install water pollution protection that would benefit himself by 1 and the downstream owner by 10; or suppose a doctor is considering whether to move his office, a move that will result in a benefit of 3 to himself and 6 to the adjacent confectionery (because of reduction in liability to the doctor); or suppose a railroad is considering whether to install spark protection that would produce a net benefit to the railroad of 6 and an equal benefit to the adjacent farmer. These Coasean-style examples can be illustrated by matrices with the same properties as Table 5. Additionally, suppose an experienced and difficult-to-replace executive is considering whether to work to produce a result that would produce a net benefit to himself of 2 and a benefit to the shareholders of 100. On the negative side of the ledger, suppose a computer hacker is considering whether to insert a virus into a company's software that would result in a loss of 5 to himself and 50 to the company; or suppose a baseball owner is considering whether to move his team from a city, a move that would result in a loss of 10 to himself and 75 to the city. All of these cases, and many others, can also be illustrated by matrices similar to the one in Table 7.⁽⁵⁷⁾

In Coase's own analysis, the threat-bargaining situation is not treated as distinctive.⁽⁵⁸⁾ In his discussion of the threat situation, Coase implies that an agreement will be reached in which the threatened party will pay something. Coase notes that "[w]hat payment would in fact be made [by the rancher] would depend on the shrewdness of the farmer and the cattle-raiser as bargainers."⁽⁵⁹⁾ Whatever one thinks about whether threat bargaining will take place and whether it will result in an agreement that will be honored, it is logically correct that the incentive for bargaining in this situation follows from the basic Coasean assumption about the mutability of payoffs. The transformation of the 2 x 1 matrix above into a 2 x 2 matrix, as shown below, illustrates the choices actually facing the parties, given mutable, rather than fixed, payoffs.

Assumptions: (1) The rancher is liable for crop damage; and (2) Cultivating crops will cause a loss of 1 to the farmer and a liability of 10 to the rancher

Grow

Row

Don't Grow

Column
I

(-1,-10)

(0,0)

(G)

Row

(NG)

Rancher

(Don't Pay)
I

(Pay)
II

(-1,-10)

(-1+x, -10-x)

(0,0)

(x, -x)

x is the amount that the rancher pays the farmer if agreement is reached and complied with by the rancher

In the Coasean matrix, the threatening party, Row, has a dominant strategy of complying with an agreement to play ii, while the threatened player, Column, has a dominant strategy of reneging on an agreement to pay.⁽⁶⁰⁾

Threat bargaining has some significant differences from bargaining involving the creation of a surplus. In the threat case, the threatened party, Column, would prefer that there were no way to get around the original payoff numbers, so that Row would simply have to play i, without having the opportunity to demand a payment from Column for doing so. In the creation of a surplus case, on the other hand, Column prefers having the opportunity to promise Row a payment in return for Row's taking Column's preferred action. There is also a difference in bargaining psychology. In the threat case, the threatening player does not have an immediate incentive to carry out the threat if the other player refuses to pay.⁽⁶¹⁾ Moreover, there is a difference in relation to efficiency. Mutability in payoffs, which allows bargaining to create a surplus, can produce efficient outcomes in situations in which standard game-theoretic analysis concludes that an inefficient result will occur. But mutability in payoffs also allows threat bargaining that creates the possibility that an inefficient outcome will occur (if Column refuses to pay and Row carries out the threat, or if Column pays and Row spitefully reneges on the promise to play the optimal strategy) in an array of situations in which standard analysis finds no obstacle to an efficient outcome. Further, even if the efficient outcome results, threat bargaining wastefully consumes resources, without the redeeming value of bargaining to create and divide a surplus.

In a 2 x 1 matrix, threats are not possible under the standard game-theoretic assumption of fixed payoffs, but such threats are possible in larger matrices under standard analysis. The aim of this section is to demonstrate how a Coasean perspective, assuming mutability of payoffs, affects standard game-theoretic threat analysis.

In standard game-theoretic analysis, it is possible in certain situations to draw a clear line between a promise that is beneficial to both parties and a threat that is beneficial if successful to the party that makes it but harmful to the other party.⁽⁶²⁾ For example, in the first matrix below Row has an incentive to unilaterally promise to play ii. In the second matrix, Row has an incentive to threaten to play ii unless Column agrees to play II.⁽⁶³⁾

(D)

Row

(C)

Column

(Defect)
I

(Cooperate)
II

(0,0)

(2,-1)

(0,0)

(1,1)

(D)

Row

(C)

Column

(Defect)
I

(Cooperate)
II

(1,2)

(2,1)

(0,0)

In common parlance, which carries over into the standard analysis, Row is making a promise in the first case because her commitment is beneficial to the other player (as well as to herself) and making a threat in the second because her commitment is inimical to the other player. A Coasean analysis changes the standard approach to both matrices: the commitment in the first matrix becomes a mixture of promise and threat, and the threat in the second matrix becomes more substantial.

First, in the Table 9 matrix, Row has an incentive to make her promise to play ii contingent upon receiving a payment (in the range of 0 to 1). While it is in Row's interest to commit to playing ii even if no payment is promised by Column, it is also in her interest to threaten to withdraw her commitment. Given this Coasean logic, the incentive for Row in this matrix is not for an unconditional promise but for a conditional promise. It is quite true that Column is better off with a conditional commitment from Row than without it, and in that sense Row's commitment still can be validly considered as a promise. But by comparison with the unconditional promise predicted by standard analysis, Coasean analysis predicts what can be described as a promise coupled with a threat from Row. At the same time, Column, who is not afforded a threat option under standard analysis, can threaten to play I unless Row promises to play ii and pay Column. The threats may or may not cancel each other out. In any event, a matrix that in standard terms offers only the opportunity for a unilateral promise is in Coasean terms a hotbed of potential threats.

In the Table 10 matrix, Row has, in Coasean terms, a more powerful threat than simply stating she will play ii unless Column agrees to play II. Row also has an incentive to demand that in addition to playing II, Column should pay Row in return for Row's promise to play i (the payment would range from 0 to 1, like the other matrix). Row's threat, in other words, is more draconian than it was in the standard analysis.⁽⁶⁴⁾

The Coasean logic of mutability makes a distinctive and counterintuitive contribution to the analysis of the Prisoners' Dilemma matrix.⁽⁶⁵⁾ The assertion that a particular set of payoffs is not given but can be altered by the parties' dealings with one another implies that, all else being equal, cooperation in the Prisoners' Dilemma is not easily effectuated; in fact, it is more difficult than one would expect.⁽⁶⁶⁾ The difficulty with cooperation in a Dilemma is not just that the given payoffs create incentives for defection, it is also that the given payoff matrices are subject to alteration by players making promises and threats to enhance their position. Even if the parties can communicate readily and rely on a well-functioning system of contract law that makes their agreements enforceable, cooperation in a Dilemma is not a foregone conclusion. Parties in a Dilemma may try to get payment from other parties to cooperate rather than simply agreeing to cooperate. The way Coasean logic disequilibrates the Dilemma can be seen in the following matrix.

(D)

Row

(C)

Column

(Defect)
I

(Cooperate)
II

(1,2)

(5,0)

(0,5)

(3,3)

This matrix is a Dilemma, differing from the Dilemma's standard symmetrical formulation only in the fact that the dominant box (1, 2), while inferior to the dominated box (3, 3) for both players, is less inferior for Column than it is for Row. A standard, non-Coasean analysis of the matrix would conclude that if communication is possible and agreements are perfectly enforceable, Row and Column will carry out promises to play ii, II and get 3 each, thus solving the Dilemma. Coasean logic upsets this analysis. Absent a preclusion of deals, Coasean logic tells us that one or both of the parties can always negotiate to circumvent the given payoff numbers. Here, Column has an incentive to tell Row that the 3, 3 outcome is a windfall to Row compared with Column and that if Row wants Column to promise to pay ii, Row will have to pay a certain amount, for example, 0.5 for Column's cooperation.⁽⁶⁷⁾ In the Prisoners' Dilemma, neither player has a threat against the other under traditional analysis. Instead, both players have an incentive to promise to play the second, dominated, strategy if the other does as well. In this situation, Coasean logic makes the analysis more complex by indicating that both sides in the Dilemma also have a threat available. Either Row, Column or both can indicate they will not agree to play the cooperative strategy unless their cooperation is paid for by the other. One might denominate this demand for payment a "qualification of a promise" rather than a "threat." Threat, however, is an appropriate term, given that the demand for payment meets the game-theoretic criterion for a threat: the player is expressing that she will take an action, which she would rather not take, in order to influence the other player's choice, thus enhancing her own payoff. If the other player stands firm in the Dilemma against paying anything to the threatening player for her cooperation, the threatener would be better off to back down and agree to cooperate without getting paid for it. If the threatener has committed herself to the threat, however (as she has an incentive to do ex ante), she will not withdraw the threat, resulting in an inefficient outcome.

A Coasean game-theoretic analysis can illuminate, though not resolve, the vexing issue of whether parties will be successful in reaching an agreement in bargaining. The previous analysis of the asymmetrical Prisoners' Dilemma is a relevant example. In the Table 11 Dilemma, will Row agree to pay Column? Even for one who has a general belief, as Coase does, that parties will usually succeed in dividing up a surplus rather than forfeiting it, the threat-bargaining case should present real difficulties.⁽⁶⁸⁾ Column's demand could be understood either as a reasonable effort to have the gain from cooperation more equally shared between the parties or as an inequitable attempt to hold up Row; one can easily imagine divisive arguments between the parties on that issue.

Under the assumption of payoff mutability, there is no longer only one point of mutual cooperation in the Prisoners' Dilemma that is the parties' single alternative to nonagreement. Both parties are able to threaten the other with a demand for payment as a condition of cooperation. Both parties have an incentive to generate arguments, such as that of Column in the asymmetrical Dilemma, in an effort to justify and indicate commitment to their threats. What is the logical focal point for agreement in Table 10? Is it the 3, 3 outcome, given that both players have threats and that 3, 3 is the result if they neutralize one another? Or is it the 1.5, 2.5 result that Column is arguing for on the basis that it splits the difference of the gains from cooperation? Or perhaps another numerical result? It would seem that there is no clear focal point for cooperation in the matrix, as understood in Coasean terms.⁽⁶⁹⁾

One argument is that parties given a wide range of alternatives, rather than a single or small number of alternatives, are more likely to agree. The idea is that continuous range bargaining fosters a sense that the only points of contention are dollar disagreements which can be bridged.⁽⁷⁰⁾ Payoff mutability means, however, that continuous-range bargaining will be over threats as well as over the creation of surpluses.

Though the circumstances of threat bargaining vary widely from situations in which the threatener's actions might be considered unexceptionable to the grossest forms of misconduct (as the doctor, baseball owner, computer hacker, and other examples in the previous section suggest), it is difficult to avoid the issues of principle that threat bargaining distinctively presents. The threatener wants the situation perceived as being akin to bargaining necessary to the creation of a surplus, but the threatened party has every reason to deny the legitimacy of threat bargaining, to point to its inefficiency and to appeal to the legal system for redress against the threatener.⁽⁷¹⁾ It would seem that there is a volatile and moral component involved in threat bargaining that makes it difficult to maintain a confident belief that agreements will be reached.

One final, significant, point about threat bargaining is that in practice (as opposed to a counterfactual world of perfect information about one's own and the other's payoffs) it is often very difficult to determine the difference between threat bargaining and bargaining over the division of a surplus. For example, is the baseball owner engaged in threat bargaining, as defined here, when he asks his city for a new stadium and says that he will leave unless it is provided? It depends upon whether moving is in the owner's interest, absent the stadium, which may be extremely difficult to determine. Inefficient threat bargaining should not be regarded as an easily identified, peripheral phenomenon. In practice, threat bargaining may often be indistinguishable from bargaining that is necessary to create a surplus.

Game-theoretic analysis of Coase's arguments should have an effect on two major areas.⁽⁷²⁾ First, one must appreciate that the fundamental Coasean assumption of mutable payoffs entails threat bargaining, as well as bargaining necessary to create a surplus. Taking threat bargaining into account leads to a substantially different interpretation of the Coasean message for law. A central implication of this Article is that in situations in which one party's preferred strategy is also the other party's preferred strategy is that bargaining between the parties is a threat to efficiency rather than a creator of it. Given this proposition, legal decision-makers must heed the total effect of the standards they promulgate, rather than simply assuming that the standards that enhance opportunities to bargain are preferable to those that preclude opportunities to bargain.⁽⁷³⁾

An underlying theme of Coasean analysis, as often presented and understood,⁽⁷⁴⁾ is a preference for legal rules that assess compensatory damages or establish property rights, rather than legal rules that mandate certain conduct.⁽⁷⁵⁾ This accepted interpretation of Coasean logic, which this Article attempts to refute, can be stated as follows: Mandatory rules, to the extent they are effective, foreclose the possibility of the parties bargaining around legal rules when it is to their advantage to do so. In Coase's spark-protection case,⁽⁷⁶⁾ therefore, a law that requires the railroad to install spark protection and imposes substantial fines for noncompliance, even in the absence of any damage caused by the sparks, may well produce an inefficient outcome because of its mandatory character. Applying this interpretation of Coasean reasoning, courts and legislatures should adhere to either property rules that provide an incentive for bargaining, or liability rules that give entitlements to the user placing the highest value on them, meanwhile avoiding mandatory regulation that precludes opportunities for bargaining.⁽⁷⁷⁾

Given the basic Coasean premise that payoffs are open to negotiation, the popular interpretation of Coasean logic, as stated above, is wrong in its condemnation of mandatory regulation. A party that benefits from taking an action that is also beneficial to the other player always has an incentive to demand payment from the other player for taking the optimal action. Once threat bargaining is recognized, caution is required in making assumptions concerning whether it would be desirable for courts and legislatures to avoid the imposition of mandatory terms. Mandatory regulation, while precluding bargaining to create a surplus, also precludes threat bargaining. This is significant because threat bargaining, unlike bargaining to create a surplus, lacks the propensity to create an efficient outcome where one would not have otherwise existed. Additionally, threat bargaining has the potential to create an inefficient outcome where the outcome would have been efficient in the absence of the opportunity for bargaining.

If one were to claim that threat bargaining is not a major issue in practice, the claimant must specify the basis of this claim. Would the claim be that human beings are somehow created so that they only seek to bargain with others to create a surplus with them, not to threaten them? This optimistic belief would seem to be both implausible and unwarranted within the basic economic model of self-seeking individuals.⁽⁷⁸⁾ In the alternative is the claim that existing social customs, institutions, and legal rules (such as a mitigation of damages requirement in contract law) condemn many instances of threat bargaining, thereby reducing its occurrence? Although this question could be answered in the affirmative, the claim is then complementary to, rather than contradictory to, the premise concerning the possible value of mandatory regulation being discussed in this Article.⁽⁷⁹⁾

If threat bargaining always resulted in agreements by the threatened party to pay, or capitulation by the threatener faced with resolve by the other party, threat bargaining would not lead to inefficient outcomes (apart from the cost associated with the bargaining itself). Threat bargaining, however, presents a real, though indeterminate, chance of an inefficient result occurring (through the threatened party and the threatener both maintaining resolve), which would not have occurred in the absence of an opportunity for the parties to bargain. The conclusion here is not that mandatory regulation is necessarily a good idea, but that it is a logical and practical mistake to believe that Coasean logic suggests that mandatory regulation is inefficient because it precludes bargaining, whereas, negotiation between parties leads to efficient outcomes. Mandatory regulation precludes bargaining--but threat bargaining is worth precluding.⁽⁸⁰⁾

The second major area in which the game-theoretic interpretation of Coasean logic is consequential for law and legal analysis involves the logical analysis of whether parties will cooperate. A game-theoretic analysis allows for a more nuanced understanding of the incentives for and the obstacles to cooperation by the parties than a transactions-cost analysis alone.

In particular, game-theoretic analysis can illuminate issues of bargaining power. For example, a game-theoretic analysis of Coasean bargaining can demonstrate how, in a legal regime with imperfect enforcement of promises, a stronger party may have an interest in reaching a nominally equal agreement that she will then defect from, rather than an unequal agreement in her favor from which she will not have a comparable opportunity to defect.⁽⁸¹⁾ Moreover, a game-theoretic analysis can be used to counter the standard claim that contract law is an ineffective vehicle for affecting wealth distribution between stronger and weaker parties. Critical work in the law and economics of housing has focused on how selective enforcement of legal standards can be used to improve the situation of tenants;⁽⁸²⁾ a game-theoretic analysis of how selective enforcement can be used to improve the situation of the weaker party in Coasean bargaining complements that literature and makes its point in a broader context.

The Coase Theorem has been difficult to formalize in a fashion that captures the flavor of Coase's original stories of neighbors and nuisances. The aim of this Article has been to give Coase's logic an accessible game-theoretic formulation that mirrors the structure and the counterintuitive quality of Coase's stories.

The fundamental Coasean point in game-theoretic terms is that the distribution of the players' payoffs for a particular combination of strategies is not fixed. Rather, the distribution is mutable, and subject to bargaining by the players. A major theme of this Article is that this Coasean logic provides different potential solutions for many matrices, including the Prisoners' Dilemma, from those provided by standard game-theoretic analysis. Coasean logic indeed means, as Coase stressed, that parties can promise each other to carry out certain actions in situations in which standard analysis does not take into account the possibility of such promises.⁽⁸³⁾ This logic of payoff mutability also, however, points out opportunities for threats not taken into account in standard analysis. Situations that in standard analysis provide incentives for promises, in a Coasean analysis also provide incentives for threats in which the promisor makes his or her cooperation contingent on a payment. Situations that in standard analysis provide incentives for threats provide incentives for more severe threats in Coasean analysis. The Coasean world is one of pervasive threats as well as promises.⁽⁸⁴⁾

Coasean logic, properly understood as a proposition about the mutability of even apparently fixed payoffs, does not support the "Coasean" folk wisdom that mandatory legal regulation is presumptively undesirable. On the contrary, the game-theoretic logic underlying the Coasean stories of ranchers, railroads, farmers, and others implies that mandatory

legal regulation can have value as a way of minimizing the threats that the mutability of payoffs makes possible.

* Assistant Professor, Rutgers University, Graduate School of Management. J.D., Harvard Law School, 1981. I would like to thank Richard Craswell, Eric Talley, and other participants at a 1995 American Law and Economics Association Conference at which an earlier version of this Article was presented for their comments. Thanks also to Marguerite Schneider for her comments.

1. Professor R.H. Coase set forth his original argument, in R.H. Coase, The Problem of Social Cost, 3 J.L. & Econ. 1 (1960) [hereinafter Coase, The Problem of Social Cost]. The basic proposition states that in the absence of transaction costs, the same efficient outcome will be reached regardless of the liability or property rules in effect. Professor Coase published two more recent essays in response to critics of that argument. See R.H. Coase, The Firm, The Market, and The Law 1-32, 95-186 (1988) [hereinafter Coase, The Firm, The Market].

2. See George J. Stigler, The Theory of Price 113 (3d ed. 1966); Herbert Hovenkamp, Marginal Utility and the Coase Theorem, 75 Cornell L. Rev. 783 (1990); Donald H. Regan, The Problem of Social Cost Revisited, 15 J.L. & Econ. 427 (1972); see also Otto A. Davis & Andrew Whinston, Externalities, Welfare, and the Theory of Games, 70 J. Pol. Econ. 241 (1962).

3. See infra Part IV; see also infra Part V for an explanation and discussion of threat bargaining.

4. See infra Table 1 for an illustration of a standard payoff matrix. The point also applies to the payoff numbers in a decision tree. For an explanation of matrices and decision trees see Ian Ayres, Playing Games with the Law, 42 Stan. L. Rev. 1291 (1990) (reviewing Eric Rasmusen, Games and Information: An Introduction to Game Theory (1989)).

5. Critical legal scholarship that has explored the indeterminacy (and political tilt) of law and economics provided a significant background for this Article. See, e.g., Mark Kelman, A Guide to Critical Legal Studies, 114-85 (1987) [hereinafter Kelman, A Guide]; Mark Kelman, Consumption Theory, Production Theory, and Ideology in the Coase Theorem, 52 S. Cal. L. Rev. 669 (1979) [hereinafter Kelman, Consumption Theory]; Duncan Kennedy & Frank Michelman, Are Property and Contract Efficient? 8 Hofstra L. Rev. 711 (1980); Pierre Schlag, An Appreciative Comment on Coase's The Problem of Social Cost: A View from the Left, 1986 Wis. L. Rev. 919. This Article is part of a series of interrelated articles that apply a critical indeterminist perspective to major models in law and economics. See Wayne Eastman, How Coasean Bargaining Entails a Prisoners' Dilemma (forthcoming in 72 Notre Dame L. Rev. (1996)) [hereinafter Eastman, Coasean Bargaining]; Wayne Eastman, Telling Alternative Stories: Heterodox Versions of the Prisoners' Dilemma, the Coase Theorem, and Supply-Demand Economics (forthcoming in 29 Conn. L. Rev. (1996)) [hereinafter Telling Alternative Stories].

7. See Coase, The Firm, The Market, supra note 1, at 15, for a particularly strong statement on this position by Coase, in which he calls the focus on the zero transaction cost case "disappointing."

8. See Hovenkamp, supra note 2, at 794-96. The transaction cost may be low enough so as not to serve as an obstacle to bargaining. See id. at 795.

14. Because this Article draws from, and frequently mentions, the works of a theorist who is very much alive, it should be noted that Coasean logic, as interpreted in this Article, should not be equated with what Professor Coase, as an individual, thinks and believes. This Article attempts to extricate a logical substrate in the "Coase Theorem" argument and to examine its reach, rather than to track the particular values that infuse Coase's work.

15. This Article's keynote argument is that parties have incentives to engage in socially suboptimal threat-bargaining that does not create a surplus, as well as optimal bargaining to create a surplus. This Article does not focus on the well-known argument that high transaction costs may provide a warrant for an activist role by the legal system. See Guido Calabresi, Transaction Costs, Resource Allocation and Liability Rules--A Comment, 11 J.L. & Econ. 67 (1968), for an early articulation of that argument. See infra notes 54-62 and accompanying text.

16. The analysis here and in the Article in general is directed toward two-person games, but the point about fixed payoffs applies generally to n-person games.

17. The sum, of course, is not subject to negotiation in the same way as the distribution.

18. This assumption (the "Coasean premise") is in my view, the essence of the logic of Coase's argument. See supra Part I.

19. In particular, there is no reliance on an assumption about zero or low transaction costs.

20. This situation--whether the parties should cooperate in adhering to an agreement or defect--describes a Prisoners' Dilemma. See Eastman, Coasean Bargaining, supra note 5, for an analysis of how the logic of Coasean bargaining, in which one person promises to pay another in return for the other adopting the first person's preferred action, is the logic of the Prisoners' Dilemma (and the significance of the link between the two). While the central theme of Coasean Bargaining is the identity between Coasean bargaining and the Prisoners' Dilemma, the central theme of this Article is the identity between the logic of the Coase Theorem and the logic of payoff indeterminacy.

23. See Coase, The Problem of Social Cost, supra note 1, at 2-8. This example, provided by Professor Coase, involves a decision that has to be made as to whether to fence the rancher's cattle to protect the farmer's crops.

25. Table 3 is simply a less abstract version of Table 2. The matrices for situations other than the one shown in Table 3 are not included in this article because the basic premise concerning Coasean logic is demonstrated with that matrix. Copies of the additional matrices are available from the author.

26. That party could be the farmer rather than the rancher. The matrix shown in Table 3 can be relabelled to cover the parallel situation discussed by Coase in which the farmer is choosing whether to plant the crops further away. See Coase, The Problem of Social Cost, supra note 1, at 4.

27. This table also applies to the scenario in which crop protection by the farmer is efficient and the rancher is liable. In that case, the farmer is Row and the rancher is Column; the farmer's payoffs are first.

28. This is in essence what Coase's "zero transaction costs" assumption is designed to achieve. See Coase, The Problem of Social Cost, supra note 1, at 2, 4, 15.

29. For example, consider the case in which the payoffs in Table 1 represent the levels of happiness of Row and Column if they do not marry (Row's strategy i), and if they do (Row's strategy ii). Cash compensation to Row for marrying Column may well be unacceptable to the players, and determining how Column can compensate Row for the marriage in units of happiness is not readily apparent. In many contexts, monetary deals are disfavored or subject to offer-asking price disparities. For an explanation of the significance of offer-asking price disparities, see Kelman, A Guide, supra note 5, at 145-48.

30. The counterfactual side-payments assumption also provides determinate predictions of the outcomes in certain matrices, while standard game-theoretic analysis does not. For example, consider the following 2 x 2 matrix:

Standard game-theoretic analysis provides a determinate outcome here only if the first move is given to either Row or Column and no interaction is possible. In this case, the player with the first move wins her preferred payoff, 4 for Row and 8 for Column. With simultaneous moves and no communication, the game is an indeterminate coordination problem. Once interaction is allowed, the standard analysis demonstrates that the player who has the first move is vulnerable to a threat by the other player to leave both of them with 0, 0, unless the first mover plays the second mover's preferred strategy. If this threat is credible, the threatener wins her preferred payoff. But threat credibility is indeterminate, so standard analysis offers no prediction regarding the outcome in this situation. See Thomas C. Schelling, The Strategy of Conflict 119-61 (1960) (defining "threat" as a statement that one will perform an act contrary to one's own as well as the other's interest if the other does not do what you want; Schelling also discusses typical moves such as threat, promise, destruction of communication and delegation of decision). Compared to this mixed and often indeterminate set of predictions associated with standard analysis, the side-payments assumption offers a simple prediction: the players will play strategy i, I (though, of course, the payoffs from their doing so are indeterminate).

31. With the assumption of unalterable payoffs, on the other hand, an increase in one player's payoff for a given combination of strategies, and a corresponding decrease for the other's, can clearly alter the outcome. For example, the standard prediction that Row will play i is altered if the 1, 1 payoffs for playing i were instead -3, 5, which would subsequently lead Row to play ii.

32. See A.C. Pigou, The Economics of Welfare 134 (4th ed. 1962) (discussing the marginal social net product using the example of "uncompensated damage done to surrounding woods by sparks from railway engines"); Coase, The Problem of Social Cost, supra note 1, at 29-34 (criticizing Pigou's contention that it would be desirable "that the railway . . . be required to compensate those who suffer damage by fires caused by railway engines"). Professor Coase countered that "if the railway could make a bargain with everyone having property adjoining the railway line and there were no costs involved in making such bargains, it would not matter whether the railway was liable for damage caused by fires or not." Id. at 31. For Professor Coase, the issue was "whether it would be desirable to make the railway liable in conditions in which it is too expensive for such bargains to be made." Id.

33. Under the standard assumption of unalterable payoffs, liability rules may of course affect the outcome that results.

34. It should be noted that the game-theoretic analysis here is a static one that does not take into account wealth effects; in this regard, as in others, it mirrors Coase's original analysis. See Regan, supra note 2, at 433-37 (discussing how effects of wealth will alter relative outputs).

36. Id. at 15 ("Another consequence of the assumption of zero transaction costs, not usually noticed, is that, when there are no costs of making transactions, it costs nothing to speed them up, so that eternity can be experienced in a split second.").

37. For example, that parties will enter into and abide by agreements in all situations in which transaction costs are less than the net benefits of agreement and compliance. See Hovenkamp, supra note 2, at 793-94.

38. This definition does not deal with the enforceability of agreements that are undesirable because of their effects on third parties.

39. These matrices assume that when both parties breach, neither one can sue the other.

40. The fact that the paying party (Column) will never have an interest in cooperating, even if the performing party (Row) performs, is because the rule of liability assumes that the worst result for the paying party is simply being compelled to pay the amount originally agreed upon. Allowing that, in this matrix it might seem that Column has an interest in cooperating with a Row who is going to defect, as long as the probability of enforcement is over 5/8, since in that case Column's payoff from cooperating will be over 1. But in any case in which the probability of enforcement is that high, Row will be cooperating and Column will be defecting.

41. At low levels of enforceability, Row will assume that Column will defect. Knowing this, the issue for Row is how high a proportion of enforcement warrants her performance. At 40% enforcement, the payoff for Row from cooperating ((.6 x 0) (.4 x 2.5)) is equal to the payoff of 1 for defecting, and Row is indifferent as to whether to cooperate.

42. I use the term "possibly correct" because of other obstacles inherent in reaching and complying with an agreement other than those analyzed here.

43. If Row and Column defect, Column gets only 1. Coase's invariance proposition about the efficient result being achieved in the zero transaction cost situation, regardless of legal rules, may be correct in this situation. Here, the proposition may be true as long as the probability of enforcement is over 3/8.

44. This position has policy implications in a situation in which there is an interest in regulating the terms of the transaction between Row and Column through, for example, minimum-wage laws. From the regulator's perspective, it is important not to allow the parties to structure payment agreements with a low probability of legal enforcement. Such agreements give Column leeway to defect and undercut the price-setting policy.

45. For present purposes, I will not examine the ethical and political issues associated with such a stance. Such issues are present in this situation as well as in the previous situation involving a calculating egoist pressing her advantage. See supra Part III.B.

46. See Duncan Kennedy, The Effect of the Warranty of Habitability on Low Income Housing: "Milking" and Class Violence, 15 Fla. St. U.L. Rev. 485 (1987) (demonstrating how selective enforcement of the warranty can benefit tenants in economically declining neighborhoods, using a graphic, non-game-theoretic analysis); see also Robin Powers Kinning, Selective Housing Code Enforcement and Low-Income Housing Policy: Minneapolis Case Study, 21 Fordham Urb. L.J. 159 (1993) (studying an instance of selective enforcement of local housing and maintenance codes); Lawrence K. Kolodney, Eviction Free Zones: The Economics of Legal Bricolage in the Fight Against Displacement, 18 Fordham Urb. L.J. 507, 531 & n.84 (1991) (using Thomas Schelling's tipping model to make a parallel point about gentrifying neighborhoods). An aim of this Article is to demonstrate how the theory that selective legal enforcement can benefit a weaker party also can be illustrated by using a game-theoretic analysis of Coasean bargaining.

47. Given the basic point of this Article about the mutability of payoffs, it should be noted in the outcome of situation two, table six, that the stronger party's cooperation is not foreordained, given the possibility that it will threaten to defect unless it receives a payment from the weaker party for cooperating. See infra Part III. But the legal system can intervene to counter this kind of threat. Again, that can be done by selectively enforcing an unconscionability-type right of the weaker party to avoid making payments, or to receive reimbursement for payments already made.

48. One may wonder whether the result shown here is an artifact of the particular numbers chosen in Table 6 or whether it has a more general application. Though no formal proof will be offered here, the answer is that the numbers can be altered, yet the result will remain the same, as long as the matrix represents a Coasean bargaining situation. See Eastman, Coasean Bargaining, supra note 5, for a discussion of how such a matrix will be a Prisoners' Dilemma. In Coasean bargaining, partial enforcement of the weaker party's promises by the legal system can always be used to create a situation in which cooperation is desirable for the stronger party, despite the fact that the weaker party is placed in a better position than he or she would have been with a less egalitarian legal system.

Applying the broad, abstract theory that selective enforcement can be used to benefit weaker parties to specific contexts is an important project, but one beyond the scope of this Article. The position emphasized here, however, by no means obviates the need for contextual, fine-grained work in areas such as rental housing. See Kennedy, supra note 46; Kinning, supra note 46; Kolodney, supra note 46. The value of the general premise inheres in countering an unduly sweeping claim that changing standards in contract law cannot affect income distribution, and in bolstering contextual work on particular legal reforms. For a related argument about the importance of examining specific economic stories, rather than simply relying on a general claim that such stories are indeterminate and politically tilted, see Eastman, Telling Alternative Stories, supra note 5.

49. As the next section of this Article discusses, the conclusion of a standard analysis that the stronger party will cooperate under these circumstances should be modified to account for the possibility that a party will threaten to defect unless he or she receives a payment for not doing so. See infra Part IV.B. As before, however, such actions by the stronger party can be countered by selective enforcement of a standard that allows the weaker party to avoid payments or receive reimbursements for payments already made. See supra notes 44-46 and accompanying text.

50. See supra Part II for the argument that Coase's logic entails the assumption of payoff mutability.

52. The largest amount R could demand from C is the difference between C's preferred payoff and her unpreferred payoff.

54. While the numbers in this matrix are negative, this is not a requirement. Any set of numbers in which the preferred strategy for Row is also the preferred strategy for Column will create the incentive for threat bargaining illustrated in this matrix.

55. Coase points out that the payment sought cannot be so high that it exceeds the cost of fencing or the value of the surrounding land to the rancher; whether these figures are less than or greater than the rancher's liability of $10 is information outside the scope of the matrix. See Coase, The Problem of Social Cost, supra note 1, at 5.

56. Coase does not describe his example as a threat. See id. Nevertheless, it fits the game-theoretic definition of a threat as a contingent commitment by a player to a course of action that she would prefer not to take.

57. In each of these examples, the amount that the other party stands to lose from the inferior strategy being played is greater than the amount the choosing party stands to lose. This is not, however, a requisite for an effective threat. Even in a situation in which the choosing party stands to gain 10 from the superior strategy and the other party stands to gain only 1, a credible threat by the choosing party to play the inferior strategy will induce a rational "threatenee" to pay up to 1 to the choosing party for committing to the preferable strategy. For a discussion of this issue, see Schelling, supra note 30, at 124-27.

60. As with Coasean bargaining over a surplus, Coasean threat bargaining can be analyzed in terms of the effects on the parties' incentives of different levels of enforcement by the legal system of their agreements. See supra notes 38-41 and accompanying text.

61. One might contend that a rational party will be unable to make a threat successfully, because the other party can simply refuse to yield, secure in the knowledge that the rational party would prefer to back down rather than to harm itself by carrying out the threat. This argument neglects the fact that a rational party who is a calculating egoist benefits from committing herself in advance to carry out the threat. If such means of advance commitment are possible, the rational party has an incentive to employ them. In addition, consideration of threat bargaining should not be ruled out because of hyperfine arguments about rationality. As Coase's own example indicates, threat issues are not limited to the Mafia or the arms race but are also found in conventional business relations. See Coase, The Problem of Social Cost, supra note 1, at 15. For a persuasive argument concerning the importance of an analysis of threats in game theory, see Schelling, supra note 30, at 123-31.

63. The matrices are from Schelling, supra note 30, at 126, 132. Both matrices can be interpreted in terms of a buyer-seller situation in which alternative parties with whom to transact are not available. In the first matrix, Column is the buyer and in the second matrix, Row is the buyer.

64. These results can be generalized, though no proof will be presented here. In any situation in which standard analysis indicates that a party has an incentive to make a promise, Coasean analysis indicates that the party also has an incentive to make a threat that the promised action will not be forthcoming, absent payment. Second, in any situation in which standard analysis indicates that a party has an incentive to make a threat in order to get the other player to play a preferred strategy, Coasean analysis indicates that the threatening party also has an incentive to demand payment from the threatened party.

65. For explanations of the canonical Prisoners' Dilemma story, in which two people would be in a better position if they could both cooperate but also both have an interest in defecting, see Robert Axelrod, The Evolution of Cooperation 7-11 (1984); Paradoxes of Rationality and Cooperation (Richmond Campbell & Lanning Sowden eds., 1985); Anatol Rapoport, Two-Person Game Theory (1966); Martin Shubik, Game Theory, Behavior, and the Paradox of The Prisoner's Dilemma: Three Solutions, 14 J. Conflict Resol. 181 (1970). It should be noted that the logic of the canonical Prisoners' Dilemma story is compatible with a wide variety of stories with political and moral implications different from the standard "cooperate"--"defect" story mentioned here. For a discussion of this point and a presentation of alternative versions of the Dilemma (and of the Coase Theorem and supply-demand equilibrium), see Eastman, Telling Alternative Stories, supra note 5.

66. There is a distinction between Coasean logic as defined in this Article, which focuses on the mutability of payoffs, and the side-payments assumption that in fact parties will work out potential agreements; the side-payments assumption leads to the conclusion that the optimal outcome will be achieved in the Dilemma.

67. Row could also demand that Column pay her for cooperating; the threat of noncooperation if money is not paid is available to both players. The purpose for changing the Dilemma matrix from the canonical, symmetrical one to the asymmetrical one here is to demonstrate how Column could generate a plausible argument for being paid to cooperate; however, it is quite true that the threat strategy is available to Row as well. Indeed, one point of Coasean analysis, as opposed to conventional game-theoretic analysis, is that both players in a 2 x 2 matrix have an incentive to make a threat. Both players in the Dilemma have an incentive to demand a payment in return for their cooperation, and even a threat completely unbacked by reason may create a commitment that the threatened party must respect.

69. See Schelling, supra note 30, at 53-80, for a discussion on the importance of focal points in allowing parties to coordinate their actions.

70. See Coase, The Firm, The Market, supra note 1, at 161-63. Such a sense that continuous-range bargaining is conducive to agreement may well be involved in Coase's own general expressions of belief that parties will succeed in reaching agreements.

71. The likelihood that the distinction between threat bargaining and bargaining necessary to the creation of a surplus may often be ambiguous in practice presents an additional problem for the parties and the legal system. For illuminating discussions of threat strategies on collection and the differences they present for the system, see Arthur Allen Leff, Injury, Ignorance and Spite--The Dynamics of Coercive Collection, 80 Yale L.J. 1, 5-10 (1970); William C. Whitford, A Critique of the Consumer Credit Collection System, 1979 Wis. L. Rev. 1047, 1143.

72. Although this Article focuses only on these areas, this does not, however, imply that the analysis is without application to other areas, such as the proper measures of damages.

73. This premise reflects the theory promulgated by Coase, although in a different context. See Coase, The Problem of Social Cost, supra note 1, at 44.

74. This theme emerged through interpretation of the Coasean analysis. It was not specifically written by Coase himself. Coase once commented that the folk wisdom of Pigou's doctrine included themes that were unstated in Pigou's own writing and a similar approach applies to the folk wisdom of Coase's doctrine. See Pigou, supra note 31.

75. A recent example of the prevalent understanding of Coase's logic is Taking Back Takings: A Coasean Approach to Regulation, 106 Harv. L. Rev. 914 (1993). Working within this framework, the author counters the claim that efficiency entails governmental liability to property owners for regulatory takings with the proposition that efficiency can also be achieved by allowing property owners to buy exemptions from regulation. See id. at 923-24.

The author's contention that purchased exemptions are a possible route to efficiency, though theoretically correct, unnecessarily yields to the popular misinterpretation of Coasean logic as opposed to mandatory regulation. Mandatory, no-exemptions regulation of certain activities, such as building within a certain distance from the shore, may preclude threat bargaining, rather than bargaining that creates a surplus. Bargaining is not necessarily something to be encouraged. Requiring compensation for regulatory takings provides an incentive to property owners to engage in threat bargaining against the government, while the alternative of allowing property owners to purchase exemptions from regulation creates an incentive for the government (or corrupt agents of the government) to engage in threat bargaining against the property owner. This problem, although acknowledged by the author, is treated as an isolated issue. See id. at 929. The value of implementing mandatory regulations of harmful uses is that it counters these types of threat bargaining and also counters threat bargaining against third parties. For example, in a regime of compensation or purchased exemptions, a property owner could demand money from his or her neighbors for ceasing or avoiding an activity that is noxious to the owner as well as to the neighbors. Simply prohibiting the activity precludes such threats.

77. See Ian Ayres & Eric Talley, Solomonic Bargaining: Dividing a Legal Entitlement To Facilitate Coasean Trade, 104 Yale L.J. 1027 (1995), for an argument that Coasean conventional wisdom is wrong in its opposition to divided entitlements and in its preference for property rules in low-transaction-costs situations.

The argument of this Article challenges Coasean conventional wisdom in a different respect, by contending that Coasean logic--though not the theory generally associated with Coase--highlights the drawbacks of bargaining.

78. See generally Robert Cooter & Stephen Marks, Bargaining in the Shadow of the Law: A Testable Model of Strategic Behavior, 11 J. Legal Stud. 225 (1982); Herbert Hovenkamp, Rationality in Law & Economics, 60 Geo. Wash. L. Rev. 293 (1992).

79. Coase's nuisance stories focused upon the situation of bilateral monopoly bargaining between parties who must deal with each other, if at all. For those who doubt that threat bargaining is a significant aspect of human interaction, I would urge that the distinction be made between bilateral monopoly and perfect competition. In the counterfactual perfect competition situation, there is no expectation that threat bargaining will be a problem; in a bilateral monopoly, on the other hand, there is an expectation that it will be pervasive. Since the Coasean focus is on a bilateral monopoly, a concern with threat bargaining is warranted.

80. Note that the efficiency rationale used here does not rely on other arguments that can be made for restricting bargaining, such as the irrationality of the parties, the moral unacceptability of having certain transactions subject to wealth effects, or the effects of the parties' transaction on third parties.

84. In this regard, there is an intriguing link between the insights of R.H. Coase and those of Thomas Schelling. Schelling pointed out the significance of threats and promises in game-theoretic strategy. See Schelling, supra note 30. Coase implicitly assumed a mutability of payoffs that leads to an even more central role for threats than in Schelling's analysis.