Absorption Paths and Equilibria in Quitting Games

TL;DR

This paper introduces absorption paths as a new way to analyze quitting games, bridging discrete and continuous time, and identifies conditions under which these paths exist as limits of equilibrium strategies.

Contribution

It defines absorption paths as an alternative to strategy profiles in quitting games and characterizes their limits as equilibrium strategies, providing new analytical tools.

Findings

Absorption paths unify discrete and continuous time analysis.

Sequentially 0-perfect absorption paths are limits of equilibrium strategies.

Certain classes of quitting games are shown to have these absorption paths.

Abstract

We study quitting games and define the concept of absorption paths, which is an alternative definition to strategy profiles that accomodates both discrete time aspects and continuous time aspects, and is parameterized by the total probability of absorption in past play rather than by time. We then define the concept of sequentially 0perfect absorption paths, which are shown to be limits of $\epsilon$-equilibrium strategy profiles as $\epsilon$ goes to 0. We finally identify a class of quitting games that possess sequentially 0-perfect absorption paths.