Mixed Strategies and Expected Utility

  • Manfred J. HollerEmail author
  • Barbara Klose-Ullmann


The analysis of mixed-strategy Nash equilibrium, offered in this chapter, builds on the concept of expected utility—which has been challenged by Allais, Kahneman-Tversky, and numerous experimental results. Here, it is applied as a theoretical tool to discuss the peculiarities of the Nash equilibrium when it is mixed as, e.g., in the Inspection Game. It is demonstrated that in the Nash equilibrium the strategy of player 1 is exclusively determined by the payoffs of player 2, and vice versa. Moreover, if the Maximin Solution of this game is in mixed strategies as well, then its payoffs are identical to the payoffs of the Nash equilibrium. In general, however, the prescribed strategies are different because in the Maximin Solution the strategy of player i depends exclusively on the payoffs of i. Arthur Miller’s “The Crucible,” the Stag Hunt Game, and Peter Handke’s “The Goalie’s Anxiety at the Penalty Kick” illustrate the results of this chapter.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of HamburgHamburgGermany
  2. 2.Center of Conflict ResolutionMunichGermany

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