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

摘要

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