A Generic Negotiation Game

Abstract

A generic Negotiation Game (NG) is used to model a conflict between two parties seeking to resolve their differences and reach a settlement. NG is a 2 × 2 non-constant-sum symmetric game that is `generic' in the sense that its payoffs, which are assumed to be cardinal, are only incompletely specified. Consequently, conclusions drawn about it are applicable to all games with which it is consistent, including such well-known games as Prisoners' Dilemma, Chicken, Deadlock and Stag Hunt. NG may be in exactly one of four mutually exclusive `states', with different pure-strategy Nash equilibria associated with each state: (1) conflict alone; (2) cooperation alone; (3) a combination of conflict and cooperation; and (4) two win-lose outcomes, each of which favors a different player. The most potent force driving NG toward state (2) is reducing the difference between winning and losing; increasing the rewards of cooperation and the penalties of conflict are not as helpful unless they occur in tandem. Normative implications of these results for encouraging negotiated settlements are discussed.

Keywords

game theory incomplete information inducement Nash equilibrium negotiation

Get full access to this article

View all access options for this article.

References

Avenhaus, Rudolf (1986) Safeguard Systems Analysis. New York: Plenum.

Brams, Steven J. (1985) Superpower Games: Applying Game Theory to Superpower Conflict. New Haven, CT: Yale University Press.

Brams, Steven J. (1990) Negotiation Games: Applying Game Theory to Bargaining and Arbitration. New York: Routledge.

Brams, Steven J. and D. Marc Kilgour (1988) Game Theory and National Security. New York: Blackwell.

Brams, Steven J. and Ben D. Mor (1991) `When Is It Rational to Be Magnanimous in Victory?' Mimeo, Department of Politics, New York University.

Fichtner, John (1986) `On Concepts for Solving Two-Person Games Which Model the Verification Problem in Arms Control', in R. Avenhaus , R.K. Huber and J.D. Kettelle (eds) Modelling and Analysis in Arms Control, pp. 421-441. Berlin: Springer-Verlag.

Holler, Manfred J. (1987) `The Maximin of Mixed Strategies in Two-Person Games.' Memo 1987-36, Institute of Economics, University of Århus, Denmark.

Holler, Manfred J. (1988) `Strategic Social Choice and Mixed-Strategy Equilibria in Two-Person Games.' Memo 1988-89, Institute of Economics, University of Århus, Denmark.

Mueller, John (1989) Retreat from Doomsday: The Obsolescence of Major War. New York: Basic.

10.

Nash, John (1951) `Non-cooperative Games', Annals of Mathematics 54: 286-295.

11.

Rapoport, Anatol , Melvin J. Guyer and David G. Gordon (1976) The 2 × 2 Game. Ann Arbor, MI: University of Michigan Press.