Subgame-perfection in quitting games with perfect information and differential equations

Subgame-perfection in quitting games with perfect information and differential equations

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Article ID: iaor20061354
Country: United States
Volume: 30
Issue: 1
Start Page Number: 51
End Page Number: 72
Publication Date: Feb 2005
Journal: Mathematics of Operations Research
Authors:
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 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 ai∈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.

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