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The cutting power of preparation

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  • Olivier Tercieux
  • Mark Voorneveld

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    Abstract

    In a strategic game, a curb set (Basu and Weibull, Econ Lett 36:141–146, 1991) is a product set of pure strategies containing all best responses to every possible belief restricted to this set. Prep sets (Voorneveld, Games Econ Behav 48:403–414, 2004) relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide sufficient conditions under which minimal prep sets give sharp predictions. These conditions are satisfied in many economically relevant classes of games, including supermodular games, potential games, and congestion games with player-specific payoffs. In these classes, minimal curb sets generically have a large cutting power as well, although it is shown that there are relevant subclasses of coordination games and congestion games where minimal curb sets have no cutting power at all and simply consist of the entire strategy space. Copyright The Author(s) 2010

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    Bibliographic Info

    Article provided by Springer in its journal Mathematical Methods of Operations Research.

    Volume (Year): 71 (2010)
    Issue (Month): 1 (February)
    Pages: 85-101

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    Handle: RePEc:spr:compst:v:71:y:2010:i:1:p:85-101

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    Related research

    Keywords: Curb sets; Prep sets; Supermodular games; Potential games; Congestion games;

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