Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach

We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions played so far. We associate with the repeated game, in a na...

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Bibliographic Details
Published inDynamic games and applications Vol. 9; no. 2; pp. 295 - 313
Main Authors Abdou, Joseph M., Pnevmatikos, Nikolaos
Format Journal Article
LanguageEnglish
Published New York Springer US 15.06.2019
Springer Nature B.V
Springer Verlag
Subjects
Asymptotic properties
Communications Engineering
Computer Systems Organization and Communication Networks
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Game Theory
Games
Humanities and Social Sciences
Linear functions
Management Science
Mathematics
Mathematics and Statistics
Networks
Operations Research
Social and Behav. Sciences
Zero sum games
Stochastic game
91A23
Discretization
Hamilton–Jacobi–Bellman–Isaacs equation
Frequency-dependent payoffs
91A25
91A15
Continuous time game
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Summary:We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions played so far. We associate with the repeated game, in a natural way, a differential game, and although the latter presents an irregularity at the origin, we prove that it has a value. We conclude, using appropriate approximations, that the asymptotic value of the original game exists in both the n -stage and the λ -discounted games and that it coincides with the value of the continuous time game.
ISSN:2153-0785
2153-0793
DOI:10.1007/s13235-018-0278-2