Publisher's Synopsis
Excerpt from Continuous Time Stopping Games With Monotone Reward Structures
The existing literature on continuous time non-zero - sum stopping games mentioned above, with the exception of Morimoto uses stochastic environments that have the Markov property. Morimoto [1986] considers cyclic stopping games. The purpose of this paper is to provide an existence theorem for Nash equilibria for a class of non-zero-sum non-cyclic stopping games in a non-markov environment. We basically extend the discrete time analysis of Mamer [1987] to a continuous time setting. Some properties of a symmetric Nash equilibrium are also characterized.
The rest of this paper is organized as follows. In Section 2 we formulate an N - person continuous time non-zero - sum stopping game. Reward processes are optional processes that may be unbounded and can take the value - 00 at t +00. A martingale approach is adopted in Section 3 to show the existence of optimal stopping policies of players under fairly general conditions. The existence of a Nash equilibrium in games with monotone payoff structures is proved in Section 4 by using Tarski's lattice theoretic fixed point theorem. We show in the same section that, for a symmetric stopping game, there always exists a symmetric equilibrium when the reward processes satisfy a monotone condition. Moreover, a symmetric equilibrium.
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