Continuous-time Games of Timing

Rida Laraki, Eilon Solan and Nicolas Vieille

The present paper addresses the question of existence of equilibrium in timing games with trivial filtration. It provides a framework that unifies the specific classes of timing games discussed in the literature. Moreover, it deals with the question of equilibrium existence in many timing games that have not been studied before.

Our first result is a general existence result for two-player games: assuming payoffs are continuous and bounded, the game has a subgame-perfect epsilon-equilibrium, for each positive epsilon.

For some classes of economic interest, we obtain stronger existence results. For symmetric games, our existence result is valid irrespective of the number of players, and the corresponding strategy profile is pure - but a symmetric epsilon-equilibrium need not exist.

We also address the issue of the existence of a Markov subgame-perfect epsilon-equilibrium, and we provide an example for the non-existence of an equilibrium in a three-player game.