Quitting games - An example

Eilon Solan, Nicolas Vieille

Research output: Contribution to journalArticlepeer-review

Abstract

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff rSi, which depends on the set 5 of players that did choose to quit. If the game never ends, the payoff to each player is zero. We exhibit a four-player quitting game, where the "simplest" equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon.

Original languageEnglish
Pages (from-to)365-381
Number of pages17
JournalInternational Journal of Game Theory
Volume31
Issue number3
DOIs
StatePublished - 2002

Keywords

  • Cyclic equilibrium
  • Games of timing
  • Stochastic games

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