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Cooperative VS. Non-cooperative Truels: Little Agreement, but Does that Matter?


  • BOSSERT, Walter
  • BRAMS, Steven J.
  • KILGOUR, D. Marc


It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, and the games may be one-round or n-round. Thus, it is never a Nash equilibrium for all players to hold their fire in any of these games, whereas in simultaneous one-round and n-round truels such cooperation, wherein everybody survives, is in both the a -core and ß -core. On the other hand, both cores may be empty, indicating a lack of stability, when the unique Nash equilibrium is one survivor. Conditions under which each approach seems most applicable are discussed. Although it might be desirable to subsume the two approaches within a unified framework, such unification seems unlikely since the two approaches are grounded in fundamentally different notions of stability.

Suggested Citation

  • BOSSERT, Walter & BRAMS, Steven J. & KILGOUR, D. Marc, 2000. "Cooperative VS. Non-cooperative Truels: Little Agreement, but Does that Matter?," Cahiers de recherche 2000-15, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2000-15

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    References listed on IDEAS

    1. Steven Brams & D. Kilgour, 1998. "Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem," Theory and Decision, Springer, vol. 45(3), pages 263-289, December.
    2. Brams, Steven J. & Kilgour, D. Mark, 1997. "The Truel," Working Papers 97-05, C.V. Starr Center for Applied Economics, New York University.
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    Cited by:

    1. David Rietzke & Brian Roberson, 2013. "The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 937-956, April.

    More about this item


    truels; noncoorative games; cores;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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