Construction of Nash equilibrium based on multiple stopping problem in multi-person game

Abstract

We consider a multi-person stopping game with players’ priorities and multiple stopping. Players observe sequential offers at random or fixed times. Each accepted offer results in a reward. Each player can obtain fixed number of rewards. If more than one player wants to accept an offer, then the player with the highest priority among them obtains it. The aim of each player is to maximize the expected total reward. For the game defined this way, we construct a Nash equilibrium. The construction is based on the solution of an optimal multiple stopping problem. We show the connections between expected rewards and stopping times of the players in Nash equilibrium in the game and the optimal expected rewards and optimal stopping times in the multiple stopping problem. A Pareto optimum of the game is given. It is also proved that the presented Nash equilibrium is a sub-game perfect Nash equilibrium. Moreover, the Nash equilibrium payoffs are unique. We also present new results related to multiple stopping problem.