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Cambridge University Press, Mathematical Structures in Computer Science, p. 1-11

DOI: 10.1017/s0960129515000365

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Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

Journal article published in 2015 by Samson Abramsky ORCID, , Viktor Winschel
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This paper is available in a repository.

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Abstract

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics.