Separable Quitting Games with Perfect Information and Differential Equations
We introduce a new approach to study subgame-perfect equilibrium payoffs in stochastic games: the differential equations approach.
We apply our approach to quitting games with perfect information. Those are sequential game in which at every stage one of n players is chosen; each player is chosen with probability 1/n
)the extension to the case where the choice is not uniform is also discussed(. The chosen player i decides whether he quits, in which case the game terminates and the terminal payoff is some vector ai in Rn, or whether he continues, in which case the game continues to the next stage. If no player ever quits, the payoff is some vector a0 in 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.