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Game Theory Behaves

*David F. Sally & Gregory Todd Jones******

*****

**Editors’ Note:**

*Almost everybody who has taken a basic course in negotiation in the last 20 years has encountered basic game theory, at least to the extent of the widely used “prisoner’s dilemma” games. But game theoreticians have been hard at work, and have come up with some disturbing findings that go way beyond the simple strategic calculations in the prisoner’s dilemma game and its equivalents. Sally and Jones analyze what has been discovered, and what it means for negotiators who need to think at least one step ahead of their counterpart and one step beyond their own biases. And if you’re a real negotiator, you’re tough enough not to be scared off by a mere equation or two.*

*This chapter is republished from the same editors’ Negotiator’s Fieldbook (American Bar Assoc. 2006). We appreciate the ABA’s courtesy in agreeing to this republication. Although this chapter was not updated for the NDR, we believe it continues to be a unique and valuable resource. Some formatting has been updated; the text of the chapter and co-author Jones’s bio are unaltered.*

Half a century ago, bargaining was central to the maturation of game theory, a field that uses mathematical theories and laboratory experiments to study strategic interaction. John Nash developed his beautiful bargaining solution by making “certain idealizations” about negotiations, namely, “that the two individuals are highly rational, that each can accurately compare his desires for various things, that they are equal in bargaining skill, and that each has full knowledge of the tastes and preferences of the other.”[1] Nash translated these idealizations into simple mathematics. First, accurate comparison of desires allows each bargainer’s preferences to be represented by a utility function, , respectively. Second, each bargainer has a threat point, the outcome if no deal occurs—in current negotiation parlance, the best alternative to a negotiated agreement, BATNA1 and BATNA2. The solution to the negotiation is the contract that maximizes the following multiplicative quantity:

More important, Nash demonstrated that his idealizations could produce a solution in not just the bargaining game but all other games as well.[2] The Nash equilibrium is a pair of strategies in a two-player game that are the best possible responses to each other. For example, there is one Nash equilibrium in the matching pennies game. Two players have a penny and must decide which face to show. One player wins if the same face (head or tail) is shown; the other wins if there is a mismatch. The stable pair of strategies consists of each player flipping his or her coin so that the presented face is chosen randomly.

Of course, Nash understood how important his idealized assumptions were to his proof. With respect to whether his model matched the reality of the bargaining game, he wrote, “The usual haggling process is based on imperfect information, the hagglers trying to propagandize each other into misconceptions of the utilities involved. Our assumption of complete information makes such an attempt meaningless.”[3] A greater part of the history of game theory over the last half century involves the analysis of whether hagglers, or just perfect players, will arrive at Nash’s solution. It happened that many players in laboratories or real markets chose the strategic equivalent of “tails” when Nash’s solution predicted “heads.” Such mismatching has led to the rise of behavioral game theory, which assumes haggling and other player imperfections are meaningful.

The purpose of this essay is to review several of the new matches between theory and reality that behavioral game theory has been responsible for in the last decade, especially those concurrences that have relevance to those who teach, study and practice the bargaining game. One historical mismatch that we assume most readers are familiar with occurred in the testing of the prisoners’ dilemma.[4] This game has served as an exemplar of the tension between cooperation and competition, between self-interest and joint maximization. Since this game and, to a lesser extent, the ultimatum game have been widely discussed and employed in the negotiation literature, we will focus on games that are not as widely known and on newly identified motives for cooperative or fair behavior.

New Games, New Motives

*Strategic Sophistication*

One of the primary pieces of advice offered to negotiators is to prepare, prepare, prepare, just like the Boy Scouts, only more. The negotiator is told to consider not only her own interests and issues, but also those of her opponent. Yet, there is a basic question that is almost never addressed: should I prepare for a prepared opponent or an unprepared opponent? This question and its more complicated variants (prepare for a prepared opponent who knows I am preparing?) involve the issue of strategic sophistication. A high degree of strategic sophistication was inherent in Nash’s idealizations: ….

For full contents please purchase The Negotiator’s Desk Reference.For full contents please purchase The Negotiator’s Desk Reference.

**Endnotes**

*

**David Sally**has a PhD in Economics from the University of Chicago and is co-author of

*The Numbers Game: Why Everything You Know About Football Is Wrong*, published by Penguin UK, translated into a dozen languages, and praised by

*The Times*as “the book that could change football forever.” He co-founded Anderson Sally LLC and has consulted with clients around the globe about football tactics, personnel moves, organizational change, and acquisitions.

(from

*The Negotiator’s Fieldbook,*ABA 2006)

**Gregory Todd Jones**, M.B.A., M.P.A., J.D., Ph.D., is Director of Research at the Interuniversity Consortium on Negotiation and Conflict Resolution and Faculty Research Fellow and Adjunct Professor of Law at Georgia State University College of Law. He directs the Computational Laboratory for Complex Adaptive Systems. During the 2005-06 academic year, Dr. Jones is Visiting Research Scholar at the Max Planck Institute for Research on Collective Goods in Bonn, Germany. Dr. Jones’ extensive multi-disciplinary scholarship has appeared in numerous law reviews as well as peer reviewed journals in law, ethics, statistics, and economics.

[1] John Nash,

*The Bargaining Problem*, 18 Econometrica 155 (1950).

[2]

*See*John Nash,

*Two-Person Cooperative Games*, 21 Econometrica 128 (1953).

[3]

*Id*. at 138.

[4] For a review of experimental results,

*see*David Sally,

*Conversation and Cooperation in Social Dilemmas: A Meta-Analysis of Experiments from 1958 to 1992*, 7 Rationality & Society 58 (1995).