A beautiful mend: a game theoretical analysis of the dormant Commerce Clause doctrine.

AuthorStearns, Maxwell L.


While the Commerce Clause neither mentions federal courts nor expressly prohibits the exercise of state regulatory powers that might operate concurrently with Congressional commerce powers, the Supreme Court has long used the dormant Commerce Clause doctrine to limit the power of states to regulate across a diverse array of subject areas in the absence of federal legislation. Commentators have criticized the Court less for creating the doctrine than for applying it in a seemingly inconsistent, or even haphazard way. Past commentators have recognized that a game theoretical model, the prisoners" dilemma, can explain the role of the dormant Commerce Clause doctrine in promoting cooperation among states by inhibiting a regime of mutual defection. This model, however, provides at best a partial account of existing dormant Commerce Clause doctrine, and sometimes seems to run directly counter to actual case results. The difficulty is not the power of game theory to provide a positive account of the cases or to provide the dormant Commerce Clause doctrine with a meaningful normative foundation. Rather, the problem has been the limited choice of models drawn from game theory to explain the conditions in which states rationally elect to avoid mutually beneficial cooperative strategies with other states. Professor Stearns shows how a state might avoid cooperation in a situation not captured in the prisoners" dilemma account to disrupt a multiple Nash equilibrium game, thus producing an undesirable mixed-strategy equilibrium in place of two or more available pro-commerce, pure Nash equilibrium outcomes. At the same time, the defecting state secures a rent that only becomes available as a consequence of the pro-commerce, pure Nash equilibrium strategies of surrounding states and that is closely analogous to quasi-rents described in the literature on relational contracting. The combined game theoretical analysis, drawing upon the prisoners' dilemma and multiple Nash equilibrium games, not only explains several of the most criticized features of the dormant Commerce Clause doctrine and several related doctrines, but also underscores the proper normative relationship between the dormant Commerce Clause doctrine and various forms of state law rent seeking.

I do not think the United States would come to an end if we lost our power to declare an Act of Congress void. I do think the Union would be imperiled if we could not make that declaration as to the laws of the several States. For one in my place sees how often a local policy prevails with those who are not trained to national views and how often action is taken that embodies what the Commerce Clause was meant to end. (1)

[I]n the 114 years since the doctrine of the negative Commerce Clause was formally adopted as [a] holding of this Court ... and in the 50 years prior to that in which it was alluded to in various dicta of the Court ... our applications of the doctrine have, not to put too fine a point on the matter, made no sense. (2)


Describing the pivotal scene in A Beautiful Mind, (3) the 2002 Academy Award winner for Best Picture, is perhaps more problematic for its mathematical than for its political incorrectness. The disturbed but brilliant John Nash, a mathematics graduate student at Princeton, is in a bar with four male classmates. The men spot a group of women that includes an extremely attractive blonde woman. One of Nash's classmates offers the following assessment: According to the teachings of Adam Smith, if all members of the group pursue the blonde woman, competition, or the invisible bond, will increase the likelihood that each man will achieve his desired goal of "scoring" with one of the women. (4) In a burst of mathematical, if not hormonal, inspiration (Nash leaves the bar without pursuing any of the women), Nash suddenly realizes that this two century-old conventional economic wisdom--suggesting that competition produces the socially optimal result--is misplaced in this context. Nash then articulates what the movie presents as his core insight, justifying his receipt, some fifty years later, of the 1994 Nobel Prize in Economics.

Nash counters his classmate by explaining that unlimited competition would prevent the five men from achieving their desired objectives. If all five men pursue the blonde woman, in their simultaneous pursuit they will block each other from succeeding with her. By pursuing that strategy, Nash continues, the men will offend the remaining women, none of whom would respond favorably to being considered a consolation prize. In this context, Nash suggests, competition threatens to produce an inferior result to that which the men could achieve if they instead coordinated their pursuits. According to Nash, if the men eschewed the blonde woman in favor of a coordinated effort in which each pursued one of the remaining women, each man's prospect for success would significantly increase.

The purpose here, of course, is not to analyze boorish male behavior. Nor is it to defend the accuracy of this particular historical account, one that, at least for this viewer, seems implausible even for an earlier generation of Princeton mathematics graduate students. (5) Rather, my objective is to compare the game theoretical insight presented in this now famous bar scene with the actual insight that gave rise to John Nash's eventual receipt of the Nobel prize.

The bar scene reveals a coordination difficulty that the men appeared to confront in their efforts to secure their individual objectives. Absent coordination, given their first choice strategies, the prospect for success by each individual actor was substantially lower than with coordination,e The problem of coordinated strategies is not uncommon to game theory; indeed it lies at the base of what is likely the most well known game--the prisoners' dilemma.

In the standard prisoners' dilemma game, the inability of two prisoners to coordinate their behavior or to enforce any prior agreements, yields an outcome for each that is inferior to that which would have been available had the prisoners followed a strategy of mutual cooperation. In this familiar game, each prisoner is informed that she will receive a modest sentence if neither prisoner rats out the other; that she will be let free if she alone rats out the other prisoner, while the other prisoner will get a maximum sentence; and that both will receive a significant sentence short of the maximum if both rat out the other. Behaving rationally, each prisoner has an incentive to defect because, regardless of what the other prisoner does, she can reduce her sentence by being an informant. (7) The problem that the prisoners' dilemma reveals is that with the given payments, (8) the players cannot achieve the potential superior outcome in which both remain silent and thus both receive modest sentences because they are unable to coordinate their behavior.

The bar scene itself does not necessarily depict a prisoners' dilemma. Without any coordinated effort, any one (or more) of the mathematics graduate students could increase his prospect of succeeding with a woman other than the blonde woman by pursuing that strategy individually. His payoff from following that strategy is therefore independent of whether the other men pursue the same strategy. (9) For our immediate purpose, however, it is sufficient to note that participants in cooperation/defection games of this sort confront incentives that threaten to produce payoffs inferior to those otherwise available if the participants are unmotivated (as might have been the case in the Princeton bar), or unable (as in the prisoners' dilemma), to coordinate their behavior.

At least one prominent game theorist has observed that the bar scene in A Beautiful Mind fails to accurately capture the true mathematical insight that resulted in Nash's receipt of the Nobel Prize. (10) Nash's foundational insight was not in recognizing that individuals can improve their positions by adopting cooperative strategies. Rather, it was in finding a solution that works in every possible game precisely because it does not require any coordination between or among the players. To illustrate, it will be helpful to introduce another familiar, but contrasting, game involving driving.

In the driving game, two drivers are trying to devise a rule or custom that optimizes their payoffs, and in doing so recognize the need to anticipate or otherwise account for the other driver's behavior. If we assume that the drivers are generally indifferent to left or right driving, but are concerned about personal safety, then the second driver will optimize her payoffs by mimicking the first driver's behavior, whether the initial regime is left or right. Unlike the prisoners' dilemma game, in which the payoffs produce a single dominant outcome--mutual defection--in the driving game, the payoffs produce two possible stable outcomes: right-right or left-left. The alternative mixed strategies--right-left or left-right--produce payoffs that either of the two drivers can improve by changing to the other's chosen regime. (11) Most importantly, the higher payoffs are achieved without the players formally coordinating their behavior. Nash's core insight was that there is a unique solution (as in the prisoners' dilemma), or a set of available solutions (as in the driving game), that is a stable equilibrium because it produces maximum payoffs for each player given the likely strategies of the other players in the absence of any coordination with the other players.

This brief introduction to cooperative and non-cooperative games provides an apt prelude to the dormant Commerce Clause doctrine and to the game theoretical analysis of that doctrine offered in this Article. The dormant Commerce Clause doctrine has long been the subject of two lines of judicial and academic criticism. First, while Article I, section 8 grants...

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