Monthly Archives: January 2007

The Benko Gambit

Here is the first of a friend’s “topic” blogs – she gave me enthusiastic permission to showcase them as they pertain to my interests. Unfortunately, the footnotes didn’t transfer. If anyone wants a specific cite, I can provide it. Next up “Property or Progeny: the Legal Status of a Human Clone.”

The Benko Gambit1

Games Theory and the Law

“Life is a form of obsessive play.”2

Game theory was initially developed in 1928 by John Von Neumann and Oskar Morgenstern as an approach to economic problems. The theory developed over time and has broadened to include the social sciences, including political science, sociology, marketing, warfare and the law.3 As noted author Karl Popper stated;

Disciplines are distinguished partly for historical reason and reasons of administrative convenience…and partly because the theories which we construct to solve our problems have a tendency to grow into unified systems. But all this classification and distinction is a comparatively unimportant and superficial affair. We are not students of some subject matter but students of problems. And problems may cut right across the borders of any subject matter or discipline.4

Game theory has been used by lawyers intuitively since the law was first practiced, and in recent years it has become more and more deliberately used in trial preparations (including which witnesses to call, which exhibits to use, and jury selection) and especially in the art of negotiating a settlement. The increasing used of alternative dispute resolution, such as arbitrations and mediations, has brought game theory to the forefront of law. This paper will give a brief overview of some of the basics and of some of the areas where game theory has been applied in the legal arena.

I. The Rules of the Game – the basics of game theory

According to one of its founders, Oskar Morgenstern, the success of game theory and its application to other disciplines is based in the fact that, unlike previous attempts to quantify social phenomena which failed, game theory is not founded in the physical sciences, which lacked the fundamental traits of social interaction (collaboration and its flip side, argument), but was taken from games of strategy, which in turn can be mathematically analyzed.5

In studying the social world, we are in need of rigorous concept. We must give precision to such terms as utility, information, optimal behavior, strategy, payoff, equilibrium, bargaining, and many more. The theory of games develops rigorous notions for all of these, and enables us to examine the bewildering complexity of society in an entirely new light. Without such precise concepts we could never hope to lift the discussion from a purely verbal state and we would forever be restricted to a very limited understanding if, indeed, we could achieve it at all.6

At the heart of game theory are two basic questions:

How should the players behave?

What should be the ultimate outcome of the game?

It should be easy to see how this correlates to the practice of law, particularly with respect to interactions between lawyers, both in a courtroom and without. These two questions lead to others: what is the “power” of a player (is it a poor client or a multi-national conglomerate), i.e. who holds the cards; to what extent can an individual affect the outcome of the game – what can the player minimally assure himself of if he receives no cooperation (i.e. “The Prisoner’s Dilemma”)?7

What are the rules of the game? Can the participants communicate with each other? Can they enter into binding agreements? Can rewards be shared with other players? What information is available to the players? And the personalities of the players must be taken into account, the mores of society (which change over time), and subjective preferences. According to Morton D. Davis,8 the most important aspect of the game is the number of players. The fewer the players, the simpler the game. The more players involved, the more complex the game and the less that game theory applies (it becomes more difficult to treat analytically).

This may explain why game theory is often used in negotiations and mediations, where fewer players are present, than in courtroom trials, with the overwhelming and changing number of players.

In a one-person game, which is the most basic, there are three types or categories: games in which nature has no active role, games where the laws of chance apply but the player is aware of the probabilities; and games where the laws of chance apply but no information is given.
In the first type, a player is simply making a choice, based on the outcome desired. The strategy chosen depends on the end result the player wishes (his utility). In the second type, the player uses the probabilities of possible events affecting his desired outcome (i.e. a farmer deciding to buy irrigation equipment takes into account his knowledge of past weather and rainfall) to achieve the optimal result. In the third type, the player makes his choice, knowing that there may be odds against him, but having no knowledge of what they might actually be.9

The next size up is the two-person game, which can be extrapolated into the basic legal paradigm of plaintiff and defendant, or two sides negotiating. There are two types of two-person games. The first is the “zero-sum” game in which wealth is neither created nor destroyed, simply transferred from one side to the other such as in poker. These games can have perfect information, or imperfect, which will lead to different strategies.10

The second type is the “non zero-sum” game, in which both players may either lose money or gain wealth (i.e. one man’s loss may NOT be another man’s gain). This can happen in situations such as union bargaining agreements in which neither side can reach agreement, and both lose. The company may have to shut down and the workers will lose their jobs.11

This paper will focus primarily on the two-person game and multi-person games in a non-perfect world, as they are the most widely used in legal situations.

According to Davis, the concept of strategy is basic to game theory. Strategy is the “complete description of how one will behave under every possible circumstance; it has no connotations to cleverness.” The number of strategies is finite. For example in chess, for each strategy used (including the Benko gambit), there is a corresponding result depending on the strategy the other player uses. These can be placed in a matrix and the outcome, win lose or draw, will be indicated. In a two-person zero-sum game of perfect information such as chess, the outcome can be known in advance. White can announce his winning strategy, and Black cannot prevent a win unless he can trick White into a deviation from his strategy. All games of perfect information are “strictly determined,” from a theorem proved by Ernst Zemelo in 1912.12

In “normal form,” the decisions are lumped together into one decision: the choice of strategy. In “extensive form,” the decisions are made one at a time. In normal form (or a simple game), the player can know the end result and thus base his/her strategy on the result desired. In extensive form, the player must analyze each decision, as it must be based on the result of the previous decision.

In a game of imperfect information, such as the child’s game of scissor, rock, paper, or in a real life negotiation, neither player knows what the other will do, but they must choose their strategies simultaneously. In this situation, the best way to approach it is to keep your strategy to yourself. In theory you can construct a matrix of strategies, but you have to assume the other player knows what strategy you have chosen. The other player can deduce your strategy based on the same logic and outguess you, and you would lose.

Knowing in advance what the other side will do can create a situation of the appearance of no-win. But the outcome of each decision from each player can be placed in a matrix, and the player should choose the strategy that has the optimal, if not perfect result. Each side will try to maximize its outcome and where they meet is called the “equilibrium point.” 13

The most classic example of game theory used in contemporary literature is the “Prisoner’s Dilemma,” first proposed by Flood and Drescher in 1950 and named by Albert Tucker shortly after.14 In the “Prisoner’s Dilemma,” the police apprehend two criminals who together have committed a serious crime. There is no direct evidence, except for the minor violation of speeding, so the prosecutor makes a proposal to each prisoner, jailed separately:
If you confess to the crime, and implicate your accomplice, I will set you free and we’ll drop the speeding charge. Your accomplice will be in prison for ten years. This offer is valid only if your accomplice does not also confess to the crime. If your accomplice also confesses, we’ll have all the proof we need, and you’ll each be jailed for five years. If neither confesses, we will have no evidence, and can only jail you on the speeding charge for one year. I am making this same offer to your accomplice.

So, if A confesses, and B does not, A gets off free, and B gets ten years. If A confesses and B does also, then each gets five years. If B confesses, and A does not, then B gets off free and A gets ten years. If neither confess, they each get one year.

A has to decide. Assuming that they have no commitment to each other, obviously each wants the best outcome for himself. If B confesses, then A knows he will be jailed for ten years if he doesn’t confess, and five years if he does. So his choice then would be to confess. If B does not confess, then A knows if he confesses he’ll be free, but if he does not confess, he’ll be jailed for a year. Therefore if B does not confess, it would be best if A confesses also. The same holds true for B. Logic demands a confession. Therefore, logically each will confess, getting five years, when if they both had not confessed, they would only have gotten one year.

Another example was used by Douglas Hofstadter in 1983. Assume one person had a bag of diamonds to sell and another had a bag of cash to buy them with. The exchange must be done in secret. If both leave a full bag, then they both are maximized. But each player will obtain a better payoff if they leave an empty bag. The seller would get either a bag of money or nothing, and the buyer would either get a diamond for free or nothing. In which case neither has lost anything. This maximizing of both strategies on an individual basis intersects at a point called the Nash Equilibrium.15

This is the Prisoner’s Dilemma. But the larger question remains: Does logic exclude rational cooperation? But what if A decides rationally and logically that not to confess would be best for both, and he knows B will also act rationally and logically, therefore it follows that neither will confess. Which logical argument is correct? According to the rules of logic, you can’t have two separate outcomes following logical paths. So therefore logically, the Prisoner’s Dilemma cannot exist. But this doesn’t take into account the irrationality of humans and the idea of mutual cooperation.

One illustration of this was in the nationally favorite reality series Big Brother II, in which four of the contestants were each offered separately money and a chance to call home. If they took the money and the call, no one else could get the call or money. If they refused, they took the chance that another would take it and they’d get nothing. If no one took the money, they all got to call home. Three of the four contestants took the offer of money and a call, and one did not. Different logic and reasoning was used by each of the contestants. One was true to her cooperative nature, and the others went for their own advantage.

Mahatma Gandhi used a unique variation of the Prisoner’s Dilemma: he neither cooperated nor defected, but used non-cooperation. Gandhi could have used defection (or violence) in his “game” against the British, but instead, by using non-cooperation, he eventually led the British to the understanding that he was honorable and reliable; although he couldn’t be trusted to use to the “rules” of the game, he could be trusted that he would always use his own rules. This strategy is more effective in building confidence in followers than a strategy of resistance.
A similar “distrategy” well known in sci-fi circles is the infamous “Kobayashi Maru” scenario from Star Trek. A game of cat and mouse used in Starfleet Academy training, no one ever beat the scenario, with the exception of a young Captain Kirk: In Kirk’s own words, he “reprogrammed the simulation so it was possible to rescue the ship.” In other words he cheated.
His response is that he “changed the conditions of the test. I got a commendation for original thinking. I don’t like to lose…I don’t believe in the no-win scenario.”16

Even scientists are getting into the picture and looking at the Prisoner’s Dilemma. Jiangfeng Du, a Chinese physicist, explores the Prisoner’s Dilemma in a new computer game with quantum rules: as is said to be true in Schroedinger’s Cat dilemma, where the cat may be equally alive or dead, the rules are changed so that each player may partly defect, and partly cooperate, the players choices are entangled. In the first iteration, one player does better than the other. In the second go-around, it is fully quantum: each player does equally well.

Similar dilemmas are faced in everyday business decisions, such as competing gas stations on price-lowering or raising, or even in operas, such as Puccini’s Tosca.17 The same holds true in the legal environment. The lawyer, judge, jury and clients all play a game. The only difference is that only one round is usually played, and the stakes vary from life itself to monetary rewards or damages. Some games are two person zero sum games, others are larger, with more players. The rest of the paper will focus on a few of the ways in which game theory is applied, and some of the problems faced in the application.

II. The Game of Life –game theory and its use in the law.

Discovery and the Prisoner’s Dilemma

The application of game theory has been used in the discovery process, both unknowingly and intentionally. Discovery can be costly, and so each side tries to determine the maximum amount needed to “win,” without going over. Game theory can provide some insights into this process. According to John K. Setear’s note in the Yale Law Journal: Discovery Abuse Under the Federal Rules: Causes and Cures, “when deciding whether to impose discovery costs on the other party, a litigant faces the ‘Prisoner’s Dilemma.’”18 Both sides have two possible strategies to pursue – make harassing discovery requests or exercise restraint. As in the Prisoner’s Dilemma, a party may gain more favorable settlement terms if he pursues the excessive discovery route; however, both sides will be worse off if they both choose that strategy. Each litigant’s costs will increase at the same rate, and the relative settlement will remain the same. And both sides will have increased costs by choosing the excessive discovery route, thus reducing their ultimate gain.19

The end result of the harassment route is similar to the Prisoner’s confessing. If one side chose to not pursue discovery, he would be at a distinct disadvantage if the other side chose to dump discovery on him. So logically, each side will choose the excessive discovery route in order to ensure that the other side doesn’t get the better of them. If the other side chooses to also do extensive discovery, then they’re even. If the other side chooses restraint, then the side choosing to overwhelm the other with discovery requests will have an advantage, and neither side wants that.

So, without some sort of outside controlling factor, discovery abuses will continue. Setear argues for the Rules: “First, they attempt to internalize some of the costs of discovery. Second, they provide the means for judges to intervene in the discovery process to prevent the unconstrained outcome of the Prisoner’s Dilemma.”20 The Rules allow two ways to intervene in the discovery process: Rules 29 and 36 encourage litigants to agree on discovery limitations or modifications, and Rule 26(c) provides for direct judicial intervention by allowing a judge, upon motion by either party, to issue a protective order limiting or prohibiting certain discovery requests.21

The Rules also help to internalize the costs of complying with discovery requests, through imposing costs on non-responsive parties, and by requiring parties to obtain information themselves that is readily available rather than forcing the other party to do it. The Rules also provide for imposition of costs on failure to adequately or truthfully answer interrogatories or requests for admissions. In addition, the Rules govern the discovery concerning experts, making sure that one party doesn’t overly benefit from the costly information gained from the other’s expert.22

Although the Prisoner’s Dilemma helps to understand and define the discovery process, judges are still reluctant to make use of the full scope of the Rules in order to minimize costs. A more stringent adherence to the Rules and the imposition of costs to the losing party on discovery motions would help alleviate the problems of the Prisoner’s Dilemma.

Game Theory and Anti-trust

“Nothing spoken or written is of any great value if the object is merely to be believed, not to be criticized and thus learn more.”23

Game theory has been increasingly used in antitrust analysis, although its role is still limited. Game theory is a favorite of economists, and when the merger guidelines were revised in 1992, game theory was at the forefront of many economic and industrial organization texts. Game theory’s influence on antitrust policy is not surprising given the strong link between economics and antitrust.

Professor Kobayashi, in his article on game theory and antitrust24 posits that there is “little reason to expect, given the current state of affairs, that game theory will play a positive role in rationalizing and clarifying the application of antitrust law.”25 Prof. Kobayashi sees the debate surrounding game theory and anti-trust as a “variant of the familiar ‘rules versus standards’ debate.”26 To Kobayashi, in a certain and errorless world, the game theory standard would be superior, but in reality, the uncertainty and imperfect enforcement make game theory too complex for ideal use.

It is a well-known tenet of game theory that the more complex the game, the less the rules apply and the less certain the outcome will be. According to Kobayashi, game theory must accurately describe behavior and performance, given a set of facts, in order to be reliably used in application in a given field. Kobayashi states that “this body of theory is close to ‘pure theory,’” and that the models have not been empirically verified.27 He feels that the conclusions drawn in game theory models tend to be “sensitive” to the problem definition and assumptions made.28

Kobayashi’s critique of game theory is based on what he sees as the weaknesses in the way economists have conducted research on organizational models. He follows Mark Blaug’s29 belief that modern economics suffers from a “reluctance to produce the theories that yield unambiguously refutable implication, followed by a general unwillingness to confront those implications with the facts.”30 Research on these types of models is characterized as “degenerating research program[s],” or those programs which are characterized by an endless addition of adjustments to accommodate new facts.31 The programs are degenerate precisely because they are able to “explain” everything, and therefore no generalizations can be drawn. “A theory that explains everything explains very little.”32

Professor Kobayashi responds to the idea that the models have a useful academic exercise basis by pointing out that the models have not been tested or subjected to meaningful empirical verification, and that absent that verification, it is premature to use these models to guide legal policy, an important point to ponder while jumping on the bandwagon of games theory.
He argues that without the empirical verification of the theories, their use should be limited, and that even if they were accurate predictors of behavior in a merger situation, there are so many models its difficult to decide which to use.

However, Kobayashi does point out that others33 suggest that “the contribution of game theory has been to illustrate complexities not recognized in older models of oligopoly behavior.”34
Tom hypothesized that considerations of these complexities make it difficult to argue the implausibility of anticompetitive outcomes, and that defendants will be less successful in avoiding antitrust litigation through the use of summary judgment motions. Kobayashi is skeptical that a decrease in successful summary judgment motions will result from the application of game theory. In looking at the Prisoner’s Dilemma, repeated applications of it might result in a cooperative outcome that is merely possible, but not necessarily the plausible outcome.

Legal Transparency and International Economic Law

William Mock wrote an article on the specialized term of legal “transparency” and its role in international economic law. As used in legal practice and theory, the term transparency means that the regulation or law and its effect and process can be seen through as easily as a clean window. If someone can understand, comply, and foresee consequences of the law then it is transparent. If not, the law is opaque.35

Transparency plays a crucial role in international economic law. It’s recognized as a key element in governmental reforms and development, such as those in emerging industrial nations as they try and gain acceptance in the world trade economy. It’s a major concept in GATT, WTO and most-favored nation status, and various treaties. Transparency has the effect of allowing businesspersons to make decisions based on all available information, rather than just on what is readily apparent. And nations are able to negotiate with other nations more effectively once they understand all the implications of economic regulation.

In the transparency model, the games of perfect information and non-perfect information are most relevant. Bridge is an example of a game of imperfect information. In the beginning, each player knows only the cards he or she holds, and not until the end of the game do they know where all the cards are. Chess is an example of a game of perfect information. Players know at all times exactly where all the pieces are on the board. There is no hidden information.36
In games of imperfect information it is necessary to analyze all information available in order to learn about the information that is hidden.37 In games of perfect information, such analysis is not necessary. In games of imperfect information, players will often signal their partners to try and convey the missing information. This is neither necessary nor possible in a perfect information game.38 In a game of imperfect information, this leads to signaling, bluffing, and deception. You can “trick” your opponent by laying a false trail. In chess, a perfect information game, deception isn’t possible. The pieces are where they stand, and the top players know it doesn’t matter what your opponent’s intentions are, it’s the potential risks and opportunities on the chess board that matter.

Mock relates game theory to transparency by introducing the concept that areas of legal regulation provide a system of players, rules and rewards, and as such are ripe for game theory. A transparent regulation equates with a game of perfect information; an opaque regulation is a game of imperfect information. In an opaque regulatory scheme, the “player” is required to seek signals from elsewhere in order to make decisions. For example, investors in developing countries will try to judge the safety of their investments from nuances (signals) of politicians and bureaucrats, rather than from the actual law or regulation.39

Information theory is a recent development that analyzes the role, process, and costs of information gathering and analysis. “Information is a valuable commodity.”40 However there are costs associated with the gathering and analysis of information. When you apply the theory of information to transparency model and games theory, the result is that the costs associated with an imperfect game become clearer. For a regulatory scheme to be transparent, the information costs must be kept to a minimum. In an opaque (imperfect) scheme, the costs of gathering information are borne by the parties involved in the transaction. These costs can often be significant, and are usually borne by the regulated party, not the government.41
For the investor, a transparent legal regime will keep his/her costs to a minimum, thus becoming the preferred investment over an opaque legal regime, which may have significant costs associated with gathering sufficient information to make an informed choice. According to Mock, “legal systems which apply the same rules to every similarly situated party and avoid[s] both confusing regulation and large grants of administrative discretion are described as embodying the Rule of Law.”42 Having a legal system that embodies the Rule of Law provides incentives for nations to adopt transparent legal regimes.

Regulatory Enforcement and Game Theory

Game theory has recently been applied to regulatory enforcement. The principles behind game theory suggest that beneficial cooperation can emerge from longstanding relationships between regulatory agencies and the industries they regulate.43

McCutcheon states that according to game theorists, the key to an effective enforcement program is for the agency to exploit the duality of being cooperative when appropriate and retaliatory when needed. However, many outside the administrative arena fear that cooperation between agency and industry.

The classic Prisoner’s Dilemma rears again. Uncertainty about the other “player’s” choice is likely to lead to the agency choosing deterrence and the business choosing evasion, even though both would be better off with mutual cooperation. According to J. Scholz,44 the agency should devise a regulatory scheme that maximizes good players by rewarding them with cooperation, applying strong deterrent measures to cheating players, and increasing incentives to reform the cheating players.

Under this scheme, strong court based enforcement policies should only be applied to the “cheaters.” To avoid the appearance of agency “capture,” Scholz suggests that agencies be subjected to close public scrutiny, such as judicial review and citizen claims. However, citizens have criticized this type of review and claim that outside scrutiny is necessary to avoid agency capture by the industry it regulates. The arrival of the citizen suit in 1970 under the Clean Air Act stemmed from the inability of agencies to enforce antipollution measures effectively.
In order to overcome some of these inherent problems, game theory has been applied. In simulations, it has been proven that playing the game over and over can lead to mutual cooperation and benefit. As long as the firm cooperates, the agency will. However, if the firm changes strategy, then the agency will do so as well. If the firm is cooperative, so is the agency. If the firm is uncooperative, then so will be the agency, and if the firm turns cooperative again, the agency will as well, as both sides are motivated by future pay-offs. This strategy can break the Prisoner’s Dilemma and bring about mutual cooperation and benefit.

The citizen suit can however put a halt to this cooperation. Under mutual cooperation strategy, the agency must be free to make the appropriate enforcement action, but the citizen suit may interfere with that process. Citizens, who might lack sufficient knowledge or information, enter the “game” and insist on deterrence when cooperation would have been more beneficial in the long run, thus putting the agency and industry back in the Prisoner’s Dilemma.

Alternative Dispute Resolution and Game Theory

“Over the next generation, I predict, society’s greatest opportunities will lie in tapping into human inclinations towards collaboration and compromise rather than stirring our proclivities for competition and rivalry.45

Alternative Dispute Resolution, or ADR, is the current popular wave in legal proceedings. It includes negotiation, mediation (including transformative, facilitative and restorative), and arbitration. Game theory is most widely relied on in the negotiation arena, but is also used in other forms of ADR.

Most of our legal conflicts are resolved through negotiation and settlement, without going through the trial process. The percentage varies, but is currently around 90-95%. Negotiation is possible in cases where the parties must cooperate to reach their goals, where they can influence each other to act in mutually beneficial ways, and when they realize that outcomes determined by others are not as preferred as those chosen by themselves.46

In negotiation, there are two basics types: competitive vs. collaborative. Competitive negotiation is about external value: Win or lose, one side gains, while the other loses. In collaborative negotiation, the emphasis is on letting both parties “win.”

Studies of the Prisoner’s Dilemma show that negotiations have two basic objectives: to achieve the party’s goals, but also to avoid being exploited.47 Playing the game repeatedly shows a strategy for avoiding exploitation and still creating cooperation. The strategy the players develop is the classic “tit-for-tat,” the same strategy used in the regulatory arena. The strategy has five rules: 1) begin cooperatively – show the other party that you desire mutual cooperation; 2) retaliate if the other side is competitive – show them that their competitiveness has negative consequences; 3) forgive if the other side becomes cooperative – signaling that mutual cooperation benefits all; 4) be clear and consistent in your approach – this way the other side knows what to expect, and parties can begin to focus on the future rather than the past; 5) be flexible – adhering to one approach beyond its effectiveness is self-limiting. This approach is nice, provocable, forgiving and transparent.48

However, some authorities argue that such a “tit-for-tat” solution might be a hindrance in bargaining and negotiating on relationship issues. To them, relationship issues do not present a Prisoner’s Dilemma and the only viable solution is cooperation.49

The zero-sum game mentioned earlier arises in various types of negotiated or arbitrated claims, such as auto accidents. An attempt is made to distribute a set amount of money from the insurance company to the party claiming injury. The amount of money stays the same, it just moves from one pocket to the other. Both sides will use the strategies mentioned earlier in order to maximize their overall gain. The negotiation process used in such claims is often called a “dance” as both parties circle around and move closer and closer to each other in a relatively fixed manner. These dances or games are games of imperfect information. Each side reveals information only in order to further his or her gain. At no time is all the information on the table for all to see. It is the equivalent of the poker player holding his cards tight to his chest, only allowing others to see when it’s to his advantage.

III. Conclusion – winning isn’t everything

As can be seen from the above, game theory at its most basic form is used throughout the legal process, much of the time unconsciously. Every player in the legal game tries to “win,” or further the interests of their side. But increasingly, some legal scholars are looking at extrapolating some of the more complex “games” into various aspects of the law, in order to gain insight into the behavior of the parties involved, to assist in furthering the interests of the parties and to help predict the outcome of various conflicts.

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