Coalgebraic Treatment of Subgame-perfect Equilibria in Infinite Games without Discounting

Samson Abramsky

We present a novel coalgebraic formulation of infinite economic non-cooperative games. We define the infinite trees of the extensive representation of the games as well as the strategy profiles by possibly infinite systems of corecursive equations. Subgame perfect equilibria are defined and proved using a novel proof principle of predicate coinduction which is related to Kozen's metric coinduction. 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 payoffs which amount to discounting the future. This suggests that coalgebras supports a more adequate treatment of infinite-horizon models in game theory and economics.

This is joint work with Viktor Winschel (University of Mannheim).