This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Solan, E. Search for Related Content

Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations

Managerial Economics and Decision Science Department, Kellogg School of Management, Northwestern University, and School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
eilons{at}post.tau.ac.il

We introduce a new approach to studying subgame-perfect equilibrium payoffs in stochastic games: the differential equations approach. We apply our approach to quitting games with perfect information. Those are sequential games in which at every stage one of n players is chosen; each player is chosen with probability 1/n. The chosen player i decides whether to quit, in which case the game terminates and the terminal payoff is some vector a_i Rⁿ, or whether to continue, in which case the game continues to the next stage. If no player ever quits, the payoff is some vector a_* Rⁿ. We define a certain differential inclusion, prove that it has at least one solution, and prove that every vector on a solution of this differential inclusion is a subgame-perfect equilibrium payoff.

Key Words: stochastic games; Dynkin games; subgame-perfect equilibrium; differential inclusions; quitting games
History: Received: September 17, 2002; revision received: March 3, 2004;