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Mixed Equilibrium: When Burning Money is Rational

Author

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  • Souza, Filipe
  • Rêgo, Leandro

Abstract

We discuss the rationality of burning money behavior from a new perspective: the mixed Nash equilibrium. We support our argument analyzing the first-order derivatives of the mixed equilibrium expected utility of the players with respect to their own utility payoffs in a 2x2 normal form game. We establish necessary and sufficient conditions that guarantee the existence of negative derivatives. In particular, games with negative derivatives are the ones that create incentives for burning money behavior since such behavior in these games improves the player’s mixed equilibrium expected utility. We show that a negative derivative for the mixed equilibrium expected utility of a given player i occurs if, and only if, he has a strict preference for one of the strategies of the other player. Moreover, negative derivatives always occur when they are taken with respect to player i’s highest and lowest game utility payoffs.

Suggested Citation

  • Souza, Filipe & Rêgo, Leandro, 2012. "Mixed Equilibrium: When Burning Money is Rational," MPRA Paper 43410, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43410
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    File URL: https://mpra.ub.uni-muenchen.de/43410/1/MPRA_paper_43410.pdf
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    References listed on IDEAS

    as
    1. Makoto Shimoji, 2002. "On forward induction in money-burning games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 637-648.
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    3. Engelmann, Dirk & Steiner, Jakub, 2007. "The effects of risk preferences in mixed-strategy equilibria of 2x2 games," Games and Economic Behavior, Elsevier, vol. 60(2), pages 381-388, August.
    4. Huck, Steffen & Muller, Wieland, 2005. "Burning money and (pseudo) first-mover advantages: an experimental study on forward induction," Games and Economic Behavior, Elsevier, vol. 51(1), pages 109-127, April.
    5. Brandts, Jordi & Holt, Charles A., 1995. "Limitations of dominance and forward induction: Experimental evidence," Economics Letters, Elsevier, vol. 49(4), pages 391-395, October.
    6. Ben-Porath, Elchanan & Dekel, Eddie, 1992. "Signaling future actions and the potential for sacrifice," Journal of Economic Theory, Elsevier, vol. 57(1), pages 36-51.
    7. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
    8. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    9. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    10. Hans Gersbach, 2004. "The money-burning refinement: With an application to a political signalling game," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 67-87, January.
    11. Ken Binmore, 1994. "Game Theory and the Social Contract, Volume 1: Playing Fair," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262023636, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Mixed Nash Equilibrium; Burning Money; Collaborative Dominance; Security Dilemma;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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