Games over Probability Distributions Revisited: New Equilibrium Models and Refinements

Stefan Rass (), Sandra König and Stefan Schauer
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Stefan Rass: LIT Secure and Correct Systems Lab, Johannes Kepler University, 4040 Linz, Austria
Sandra König: Austrian Institute of Technology, Center for Digital Safety & Security, Giefinggasse 4, 1210 Vienna, Austria
Stefan Schauer: Austrian Institute of Technology, Center for Digital Safety & Security, Giefinggasse 4, 1210 Vienna, Austria

Games, 2022, vol. 13, issue 6, 1-26

Abstract: This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Nash equilibrium, as a proposed solution concept in this generalized class of games.

Keywords: game theory; security strategy; generalized game; loss distributions; decision making; Nash equilibrium; lexicographic optimization (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2022
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