Games over Probability Distributions Revisited: New Equilibrium Models and Refinements

IF 0.6 Q4 ECONOMICS Games Pub Date : 2022-12-01 DOI:10.3390/g13060080
S. Rass, Sandra König, S. Schauer
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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.
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重新审视概率分布上的博弈:新的均衡模型及其改进
这篇文章概述了博弈论的最新进展,其收益是概率分布,而不是实数,并且在一组(适当限制但密集的)分布上定义和计算了它们的平衡。虽然用实值效用函数定义游戏模型的经典方法在许多领域都取得了惊人的成功,但来自安全领域的一些用例揭示了经典实值游戏模型的缺点。这些问题促使使用概率分布作为一个更复杂的对象来表示收入。由此产生的一类游戏显示了经典游戏中没有遇到的各种现象,例如具有连续回报函数但仍然没有平衡的游戏,或者是零和但虚构游戏不收敛的游戏。我们讨论了如何定义这类对策以允许定义均衡的适当限制,并展示了字典纳什均衡的概念,作为这类广义对策中的一个拟议解概念。
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来源期刊
Games
Games Decision Sciences-Statistics, Probability and Uncertainty
CiteScore
1.60
自引率
11.10%
发文量
65
审稿时长
11 weeks
期刊介绍: Games (ISSN 2073-4336) is an international, peer-reviewed, quick-refereeing open access journal (free for readers), which provides an advanced forum for studies related to strategic interaction, game theory and its applications, and decision making. The aim is to provide an interdisciplinary forum for all behavioral sciences and related fields, including economics, psychology, political science, mathematics, computer science, and biology (including animal behavior). To guarantee a rapid refereeing and editorial process, Games follows standard publication practices in the natural sciences.
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