Theory and Decision

, Volume 44, Issue 1, pp 37–66 | Cite as

Nash Equilibrium with Lower Probabilities

  • Ebbe Groes
  • Hans Jørgen Jacobsen
  • Birgitte Sloth
  • Torben Tranaes


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 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Ebbe Groes
    • 1
  • Hans Jørgen Jacobsen
    • 1
  • Birgitte Sloth
    • 1
  • Torben Tranaes
    • 1
  1. 1.Institute of Economics, University of CopenhagenCopenhagen K.Denmark

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