The APS approach for undiscounted quitting games

Abstract

Characterizing and explicitly computing equilibria of undiscounted dynamic games have been a challenge for many years. In this paper, we study quitting games, which are stopping games where the terminal payoff does not depend on the stage of termination. We adapt the recursive approach of Abreu, Pearce, and Staccheti (1990) to characterize a certain subset of the set of subgame-perfect ε-equilibrium payoffs. Our approach is based on the novel representation of strategy profiles through absorption paths, which was developed in Ashkenazi-Golan, Krasikov, Rainer, and Solan (2024), and our characterization focuses on absorption paths in which exactly one player randomizes between quitting and continuing at any point in time. Since quitting games form a special case of both stopping games and stochastic games, our approach may be useful in studying more general classes of these games.