Mixed Strategies and Expected Utility

Manfred J. Holler () and Barbara Klose-Ullmann
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Manfred J. Holler: University of Hamburg
Barbara Klose-Ullmann: Center of Conflict Resolution

Chapter Chapter 10 in Scissors and Rock, 2020, pp 165-194 from Springer

Abstract: Abstract The analysis ofStrategymixed-mixed-strategyMixed strategyNash equilibrium,Nash equilibrium offered in this chapter, builds on the concept of expected utilityUtilityexpected-—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 equilibriumNash equilibrium when it is mixed as, e.g., in the Inspection Game.Inspection Game It is demonstrated that in the Nash equilibriumNash equilibrium the strategy of player 1 is exclusively determined by the payoffs of player 2, and vice versa. Moreover, if the Maximin SolutionMaximin Solution of this game is in mixed strategiesMixed strategy as well, then its payoffs are identical to the payoffs of the Nash equilibrium.Nash equilibrium In general, however, the prescribed strategies are different because in the Maximin SolutionMaximin Solution the strategy of player i depends exclusively on the payoffs of i. Arthur Miller’s “The Crucible,” the Stag Hunt Game,Stag Hunt Game and Peter Handke’sHandke, Peter “The Goalie’s AnxietyGoalie’s Anxiety at the Penalty Kick” illustrate the results of this chapter.

Date: 2020
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DOI: 10.1007/978-3-030-44823-3_10

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