Quitting games - An example

Les jeux d'arrêt sont des jeux séquentiels où, à chaque étape, chacun des joueurs peut décider d'arrêter ou de continuer. Le jeu s'arrête dès lors que l'un au moins des joueurs décide de s'arrêter. Le paiement reçu alors par les joueurs dépend de l'ensemble des joueurs qui ont choisi de s'arrêter à cette date. Si le jeu ne s'arrête jamais, le paiement est nul. Nous étudions un jeu à quatre joueurs. Dans ce jeu, les équilibres les plus simples sont périodiques de période deux. Par ailleurs, nous utilisons des outils géométriques pour montrer que les techniques utilisées pour les jeux à trois joueurs ne peuvent être adaptées au cas général.Jeux d'arrêt;Jeux stochastiques;Equilibre

Quitting games - an example

Quitting games are I-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 , which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.stopping games; equilibrium; stochastic games

Absorption paths and equilibria in quitting games

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

Quitting Games

Quitting games are sequential games in which, at any stage, each player has the choice between continuing and quitting. The game ends as soon as at least player chooses to quit; player i then receives a payoff r, 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. We prove the existence of cyclic E-equilibrium under some assumptions on the payoff function (r sub s). We prove on an example that our result is essentially optimal. We also discuss the relation to Dynkin's stopping games, and provide a generalization of our result to these games.

Quitting Games.

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.Quitting games; uniform equilibrium; Dynkin's stopping games; n-player stochastic games;

Equilibria in Quitting Games and Software for the Analysis

A quitting game is an undiscounted sequential stochastic game, with finitely many players. At any stage each player has only two possible actions, continue and quit. The game ends as soon as at least one player chooses to quit. The players then receive a payoff, which depends only on the set of players that did choose to quit. If the game never ends, the payoff to each player is zero. In this thesis we give a detailed introduction to quitting games. We examine the existing results for the existence of equilibria and improve an important result from Solan and Vieille stated in their article “Quitting Games” (2001). Since there is no software for the analysis of quitting games, or for stochastic games with more than two players, we provide algorithms and programs for symmetric quitting games, for a reduction by dominance and for the detection of a pure, instant and stationary epsilon-equilibrium