# Negotiation Games: Applying Game Theory to Bargaining and Arbitration

## Steven J. Brams

Language: English

Pages: 320

ISBN: 0415903386

Format: PDF / Kindle (mobi) / ePub

This book shows how game theory can illuminate the strategic choices of players who have both intersecting and conflicting interests in negotiations. It uses examples ranging from biblical stories to political superpower conflict, such as the 1962 Cuban missile crisis, the 1973 Yom Kippur War, and the 1980-1 Solidarity movement in Poland. Although the theory used is mathematical, technical details are eschewed to make the models and applications accessible to social (especially political) scientists and practitioners. This book should be of interest to students and professionals of international relations, politics, and economics.

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tat-for-tit ( /P), P is the resultant outcome, for the choice of P by the mother implies the choice of by the impostor under tat-for-tit. As can be seen from Figure 1.6, this yields a payoff of (3,4)—the next-best outcome for the mother, the best for the impostor (in their eyes, anyway)—which is shown in the P row and /P column of Figure 1.7. What are the game-theoretic implications of the preference assump- 22 NEGOTIATIONS IN THE BIBLE Figure 1.7. Payoff matrix of Solomon’s game Key:

S’s possible reservation prices are 1 or 2, and B’s 2 or 3. In other words, each player may have either a high or low reservation price— with S’s high price coinciding with B’s low price—and this is common knowledge. Given that the players prefer an agreement with zero profit to no agreement (e.g., for the purpose of promoting better future relations), then it is easy to see that both players will always choose 2, regardless of their reservation prices, under the Chatterjee-Samuelson procedure. I

Tversky, and Robert Wilson (eds.) (1995). Barriers to Conflict Resolution. New York: W.W.Norton. Balinski, Michel L., and H.Peyton Young (2001). Fair Representation: Meeting the Ideal of One Man, One Vote, 2nd ed. New Haven, CT: Yale University Press. Bates, Robert H., Avner Greif, Margaret Levi, Jean-Laurent Rosenthal, and Barry R. Weingast (eds.) (1998). Analytic Narratives. Princeton, NJ: Princeton University Press. Brams, Steven J. (1992). “A Generic Negotiation Game,” Journal of Theoretical

scramble to leave the initial outcome first. In either event, a rational choice is dictated not only by one’s own game-tree analysis but by that of the other player as well, which may cause one to override one’s own (one-sided) rational choice. Henceforth, I assume that a final outcome reflects the two-sided analysis that both players would make of each other’s rational choices, in addition to their own. In the case of outcomes (2,4) and (4,2), it is impossible to say a priori which player would

contains only Pareto-superior outcomes, neither player has any threat strategies. In particular, neither player can credibly threaten its opponent in a total-conflict (zero-sum) game. Thus, the Paretoinferiority of at least one outcome is necessary for the effective exercise of threat power in a game. Providing that the sufficient conditions given under Cases 1 and 2 are met, the Pareto-inferior outcomes become breakdown outcomes for T. Furthermore, as indicated for each case, 2. T can always