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Binary games with many players

Listed author(s):
  • 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

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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 28 (2006)
Issue (Month): 1 (May)
Pages: 125-143

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Handle: RePEc:spr:joecth:v:28:y:2006:i:1:p:125-143
DOI: 10.1007/s00199-005-0611-z
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