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Binary games with many players


  • Flavio Menezes


  • Rohan Pitchford



We examine a problem with n players each facing the same binary choice. One choice is superior to the other. The simple assumption of competition - that an individual’s payoff falls with a rise in the number of players making the same choice, guarantees the existence of a unique symmetric equilibrium (involving mixed strategies). As n increases, there are two opposing effects. First, events in the middle of the distribution - where a player finds itself having made the same choice as many others - become more likely, but the payoffs in these events fall. In opposition, events in the tails of the distribution - where a player finds itself having made the same choice as few others - become less likely, but the payoffs in these events remain high. We provide a sufficient condition (strong competition) under which an increase in the number of players leads to a reduction in the equilibrium probability that the superior choice is made. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Flavio Menezes & Rohan Pitchford, 2006. "Binary games with many players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 125-143, May.
  • Handle: RePEc:spr:joecth:v:28:y:2006:i:1:p:125-143
    DOI: 10.1007/s00199-005-0611-z

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    Cited by:

    1. Kets, W., 2007. "The Minority Game : An Economics Perspective," Discussion Paper 2007-53, Tilburg University, Center for Economic Research.
    2. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.

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    Binary choices; Competition; Entry.;


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