Article

Theory and Decision

, Volume 44, Issue 1, pp 37-66

Nash Equilibrium with Lower Probabilities

  • Ebbe GroesAffiliated withInstitute of Economics, University of Copenhagen
  • , Hans Jørgen JacobsenAffiliated withInstitute of Economics, University of Copenhagen
  • , Birgitte SlothAffiliated withInstitute of Economics, University of Copenhagen
  • , Torben TranaesAffiliated withInstitute of Economics, University of Copenhagen

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Abstract

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.

Knightian uncertainty ambiguity mixed strategy Nash equilibrium lower probabilities belief functions prisoner's dilemma