Games over Probability Distributions Revisited: New Equilibrium Models and Refinements
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 mod...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Games |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-4336/13/6/80 |
| _version_ | 1797458102492069888 |
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| author | Stefan Rass Sandra König Stefan Schauer |
| author_facet | Stefan Rass Sandra König Stefan Schauer |
| author_sort | Stefan Rass |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T16:32:16Z |
| format | Article |
| id | doaj.art-5fa34a6298fe4483a545c110fd7e0f8a |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-03-09T16:32:16Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-5fa34a6298fe4483a545c110fd7e0f8a2023-11-24T14:59:59ZengMDPI AGGames2073-43362022-12-011368010.3390/g13060080Games over Probability Distributions Revisited: New Equilibrium Models and RefinementsStefan Rass0Sandra König1Stefan Schauer2LIT Secure and Correct Systems Lab, Johannes Kepler University, 4040 Linz, AustriaAustrian Institute of Technology, Center for Digital Safety & Security, Giefinggasse 4, 1210 Vienna, AustriaAustrian Institute of Technology, Center for Digital Safety & Security, Giefinggasse 4, 1210 Vienna, AustriaThis 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.https://www.mdpi.com/2073-4336/13/6/80game theorysecurity strategygeneralized gameloss distributionsdecision makingNash equilibrium |
| spellingShingle | Stefan Rass Sandra König Stefan Schauer Games over Probability Distributions Revisited: New Equilibrium Models and Refinements Games game theory security strategy generalized game loss distributions decision making Nash equilibrium |
| title | Games over Probability Distributions Revisited: New Equilibrium Models and Refinements |
| title_full | Games over Probability Distributions Revisited: New Equilibrium Models and Refinements |
| title_fullStr | Games over Probability Distributions Revisited: New Equilibrium Models and Refinements |
| title_full_unstemmed | Games over Probability Distributions Revisited: New Equilibrium Models and Refinements |
| title_short | Games over Probability Distributions Revisited: New Equilibrium Models and Refinements |
| title_sort | games over probability distributions revisited new equilibrium models and refinements |
| topic | game theory security strategy generalized game loss distributions decision making Nash equilibrium |
| url | https://www.mdpi.com/2073-4336/13/6/80 |
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