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

Published online by Cambridge University Press:  23 July 2015

SAMSON ABRAMSKY and
VIKTOR WINSCHEL
SAMSON ABRAMSKY
Affiliation:
Department of Computer Science, University of Oxford, Oxford, Oxfordshire, U.K. Email: samson@comlab.ox.ac.uk
VIKTOR WINSCHEL
Affiliation:
Department of Management, Technology, and Economics, ETH Zurich, Zurich, Switzerland Email: viktor.winschel@googlemail.com
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Abstract

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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.

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