Absorption paths and equilibria in quitting games

Galit Ashkenazi-Golan, Ilia Krasikov, Catherine Rainer, Eilon Solan

Research output: Contribution to journalArticlepeer-review

Abstract

We study quitting games and introduce an alternative notion of strategy profiles—absorption paths. An absorption path is parametrized by the total probability of absorption in past play rather than by time, and it accommodates both discrete-time aspects and continuous-time aspects. We then define the concept of sequentially 0-perfect absorption paths, which are shown to be limits of ε-equilibrium strategy profiles as ε goes to 0. We establish that all quitting games that do not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) have a sequentially 0-perfect absorption path. Finally, we prove the existence of sequentially 0-perfect absorption paths in a new class of quitting games.

Original languageEnglish
JournalMathematical Programming
DOIs
StateAccepted/In press - 2022
Externally publishedYes

Keywords

  • Continuous equilibria
  • Linear complementarity problems
  • Q-matrices
  • Quitting games
  • Stochastic games

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