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Quitting Games

Abstract : Quitting games are n-player sequential games in which, at any stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; player i then receives a payoff riS, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is 0. The paper has four goals: (i) We prove the existence of a subgame-perfect uniform {varepsilon}-equilibrium under some assumptions on the payoff structure; (ii) we study the structure of the {varepsilon}-equilibrium strategies; (iii) we present a new method for dealing with n-player games; and (iv) we study an example of a four-player quitting game where the "simplest" equilibrium is cyclic with Period 2. We also discuss the relation to Dynkin's stopping games and provide a generalization of our result to these games.
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Submitted on : Thursday, March 18, 2010 - 4:47:16 PM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Nicolas Vieille, Eilon Solan. Quitting Games. Mathematics of Operations Research, INFORMS, 2001, Vol.26,n°2, pp.265-285. ⟨10.1287/moor.26.2.265.10549⟩. ⟨hal-00465043⟩

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