Cooperative Strategies in Stopping Games

Abstract

This article considers a cooperative approach to 2-player stopping games. It is assumed that the players cooperate in such a way as to maximise the sum of their expected payoffs. Hence, the value of the game to a coalition of both players is given by the optimal expected reward in an auxiliary problem, which involves the double stopping of a Markov chain by an individual. The value of the game is defined using a recursive procedure based on the form of the subgames played at each moment. The concept of Shapley value is used to define the value of a subgame. It is shown that, in games where one player always has priority, the Shapley value of the cooperative game is simply the unique Nash value of the game. In games involving random priority, players must coordinate their actions and use side payments to achieve the Shapley value. The side payments and coordination may be described in a preplay agreement made between the players. Aspects of the dynamic rationality of such agreements are considered using the concept of subgame consistency. An example based on the job search problem is given