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

TL;DR

This paper introduces a coalgebraic approach to analyze infinite extensive games and their subgame perfect equilibria without relying on discounting or continuity assumptions, offering a more general framework.

Contribution

It develops a coalgebraic formulation for infinite games and strategy profiles, and introduces a novel proof principle of predicate coinduction for equilibrium analysis.

Findings

Characterizes all subgame perfect equilibria in the dollar auction game.

Proves a one-deviation principle without discounting assumptions.

Demonstrates coalgebra's suitability for infinite-horizon economic models.

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. 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. 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.