Separable
Quitting Games with Perfect Information and Differential Equations

Eilon
Solan

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 *a _{i}* in

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.