On comparing equilibrium and optimum payoffs in a class of discrete bimatrix games

نویسنده

  • William Stanford
چکیده

In an m 3 m bimatrix game, consider the case where payoffs to each player are randomly 1 2 drawn without replacement, independently of payoffs to the other player, from the set of integers 1,2, . . . ,m m . Thus each player’s payoffs represent ordinal rankings without ties. In such ‘ordinal 1 2 randomly selected’ games, assuming constraints on the relative sizes of m and m and ignoring 1 2 any implications of mixed strategies, it is shown that payoffs to pure Nash equilibria (seconddegree) stochastically dominate payoffs to pure Pareto optimal outcomes. Thus in such games where pure strategy sets do not differ much in size and payoffs conform with concave von Neumann-Morgenstern utility functions over ordinally ranked outcomes, players would prefer (ex ante) a ‘random pure strategy Nash equilibrium payoff’ to a ‘random pure Pareto optimal outcome payoff’.  2000 Elsevier Science B.V. All rights reserved.

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عنوان ژورنال:
  • Mathematical Social Sciences

دوره 39  شماره 

صفحات  -

تاریخ انتشار 2000