The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Zero-Sum Games

  • Michael Bacharach
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1658

Abstract

Zero-sum games are to the theory of games what the twelve-bar blues is to jazz: a polar case, and a historical point of departure. A game is a situation in which (i) each of a number of agents (players) has a set of alternative courses of action (strategies) at his disposal; (ii) there are outcomes which depend on the combination of the players’ actions and give rise to preferences by the players over these combinations; (iii) the players know, and know that each other knows, these preferences. (Strictly, such a situation is a game of complete information in normal form: these qualifications should henceforth be understood.) In the case which dominates the literature of zero-sum games there are two players, A and B say, each with a finite set of strategies, and their preferences can be represented by von Neumann–Morgenstern utilities. The preference structure can then be displayed in a payoff matrix, whose (i, j)th entry (uij, υij) gives the expected utilities or payoffs of A and B respectively for A using his ith strategy and B using his jth. A game of this type in which uij + υij = 0 for all i, j is known as a zero-sum matrix game (henceforth simply zero-sum game). In a zero-sum game the players have exactly opposed preferences over strategy-pairs. Hence there is no scope for the pair of them to act as a pair – there is nothing for them to cooperate about. The theory of cooperative zero-sum games is thus an empty box; zerosum games are non-cooperative games, and each player must choose in uncertainty of the other’s choice.

This is a preview of subscription content, log in to check access

Bibliography

  1. Colman, A. 1982. Game theory and experimental games. Oxford: Pergamon.Google Scholar
  2. Ellsberg, D. 1956. Theory of the reluctant duelist. American Economic Review 46: 909–923.Google Scholar
  3. Gale, D. 1951. Convex polyhedral cones and linear inequalities. In Activity analysis of production and allocation, ed. T.C. Koopmans. New York: Wiley.Google Scholar
  4. Johansen, L. 1981. Interaction in economic theory. Economie Appliquee 34(2–3): 229–267.Google Scholar
  5. Von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Michael Bacharach
    • 1
  1. 1.