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Mixed Equilibrium: When Burning Money is Rational

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  • Souza, Filipe
  • Rêgo, Leandro
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    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43410.

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    Date of creation: 10 Feb 2012
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    Handle: RePEc:pra:mprapa:43410

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

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    1. Engelmann, Dirk & Steiner, Jakub, 2007. "The effects of risk preferences in mixed-strategy equilibria of 2x2 games," Games and Economic Behavior, Elsevier, Elsevier, vol. 60(2), pages 381-388, August.
    2. Huck, S. & Müller, W., 2005. "Burning money and (pseudo) first-mover advantages: An experimental study on forward induction," Open Access publications from Tilburg University urn:nbn:nl:ui:12-171348, Tilburg University.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262061414, December.
    4. Makoto Shimoji, 2002. "On forward induction in money-burning games," Economic Theory, Springer, Springer, vol. 19(3), pages 637-648.
    5. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262582384, December.
    6. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(2), pages 476-496, August.
    7. Brandts, Jordi & Holt, Charles A., 1995. "Limitations of dominance and forward induction: Experimental evidence," Economics Letters, Elsevier, Elsevier, vol. 49(4), pages 391-395, October.
    8. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, Elsevier, vol. 36(1), pages 31-56, July.
    9. Ken Binmore, 1994. "Game Theory and the Social Contract, Volume 1: Playing Fair," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262023636, December.
    10. Hans Gersbach, 2004. "The money-burning refinement: With an application to a political signalling game," International Journal of Game Theory, Springer, Springer, vol. 33(1), pages 67-87, January.
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