Equilibrium payoffs in repeated two-player zero-sum games of finite automata

Repeated two-player zero-sum games of finite automata are studied. The players are charged a penalty proportional to the size of their automata to limit the complexity of strategies they can use. The notion of bounded computational capacity equilibrium payoff is thus transferred to the case of zero-...

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Bibliographic Details
Published in:International journal of game theory 2019-06, Vol.48 (2), p.423-431
Main Author: Baskov, O. V.
Format: Article
Language:English
Subjects:
Automata theory
Behavioral/Experimental Economics
Computation
Convergence
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equilibrium
Game Theory
Games
Operations Research/Decision Theory
Original Paper
Social and Behav. Sciences
Zero sum games
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Summary:Repeated two-player zero-sum games of finite automata are studied. The players are charged a penalty proportional to the size of their automata to limit the complexity of strategies they can use. The notion of bounded computational capacity equilibrium payoff is thus transferred to the case of zero-sum games. It is proved that the set of bounded computational capacity equilibrium payoffs contains exactly one value, namely the value of the one-shot game, or, equivalently, that the value of the game with penalty approaches the value of the one-shot game as the penalty goes to zero. An estimate of the rate of convergence is also provided.
ISSN:0020-7276
1432-1270
DOI:10.1007/s00182-018-0634-x