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

  • Authors:

  • Eilon Solan

  • Affiliations:

  • -

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2005

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Abstract

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 ofn players is chosen; each player is chosen with probability 1/ n. The chosen playeri decides whether to quit, in which case the game terminates and the terminal payoff is some vectora 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 vectora* ?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.