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Bluffing as a Mixed Strategy

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  • Thomas Norman

Abstract

In von Neumann and Morgenstern's sample model of poker, equilibrium has the first player bet with high and low hands, and check with intermediate hands. The second player then calls if his hand is sufficiently high. Betting by the low hands is interpreted as bluffing, and is a pure strategy. Here we show that this equilibrium is nongeneric, in the sense that it ceases to exist if the first player is allowed to choose among many possible bets, rather than just one. Moreover, Newman's solution for this case - which also has pure-strategy bluffing - is shown not to be a sequential equilibrium. However, a modified solution - where low hands bluff using mixed strategies - is a sequential equilbrium.

Suggested Citation

  • Thomas Norman, 2012. "Bluffing as a Mixed Strategy," Economics Series Working Papers 590, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:590
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    References listed on IDEAS

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    1. Marcel Dreef & Peter Borm & Ben van der Genugten, 2003. "On Strategy and Relative Skill in Poker," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 83-103.
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    More about this item

    Keywords

    Poker; Game theory; Mixed strategies; Perfect Bayesian equilibrium; Sequential equilibrium;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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