On Perfectly Coalition-proof Nash Equilibria

  • Bezalel Peleg


The most prominent solution in the theory of noncooperative games is the Nash equilibrium. However, there are some fundamental problems with the interpretation and application of it that led to many refinements (see, e.g., Selten, 1975). The following difficulty concerning the application of Nash equilibria has been pointed out in Bernheim, Peleg, and Whinston [1987]. Let g = (∑ 1, …, ∑ n ; h 1, …, h n ) be a game in strategic form and assume that g has two or more equilibria. In order to choose an equilibrium point the players have to meet and coordinate their strategies. Thus, from a theoretical point of view, preplay communication is needed for the implementation of Nash equilibria. However, one may argue that the players of g may use a theory that selects a unique equilibrium for each game in order to avoid preplay communication (see Harsanyi, 1975). This is possible only at a theoretical level, because in real life games there are almost always possibilities for direct or indirect communication, and there are no means to prevent coalitions of players from coordinating their strategies. In summary, in important classes of noncooperative environments preplay communication is unavoidable and, therefore, coalitions may coordinate their strategies and deviate from an equilibrium.


Nash Equilibrium Linear Order Perfect Information Simple Game Subgame Perfect Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bernheim, B. D., B. Peleg and M. D. Whinston (1987) ‘Coalition-proof Nash Equilibria I: Concepts’, Journal of Economic Theory, 42, pp. 1–12.CrossRefGoogle Scholar
  2. Bernheim, B. D. and M. D. Whinston (1987) ‘Coalition-proof Nash Equilibria II: Applications’, Journal of Economic Theory, 42, pp. 13–29.CrossRefGoogle Scholar
  3. Gale, D. (1953) ‘A Theory of N-Person Games with Perfect Information’, Proceedings of the National Academy of Sciences (USA) 39, 496–501.CrossRefGoogle Scholar
  4. Harsanyi, J. C. (1975) ‘The Tracing Procedure: a Bayesian Approach to Defining a Solution for N-Person Noncooperative Games’, International Journal of Game Theory, 4, pp. 61–94.CrossRefGoogle Scholar
  5. Ichiishi, T. (1986) ‘stable Extensive Game Forms with Perfect Information’, International Journal of Game Theory, 15, pp. 163–74.CrossRefGoogle Scholar
  6. Moulin, H. (1983) The Strategy of Social Choice (Amsterdam: North-Holland).Google Scholar
  7. Peleg, B. (1984) Game Theoretic Analysis of Voting in Committees (Cambridge: Cambridge University Press).CrossRefGoogle Scholar
  8. Selten, R. (1975) ‘Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games’, International Journal of Game Theory, 4, pp. 25–55.CrossRefGoogle Scholar

Copyright information

© Mukul Majumdar 1992

Authors and Affiliations

  • Bezalel Peleg

There are no affiliations available

Personalised recommendations