Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem

Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem

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Article ID: iaor20134329
Volume: 3
Issue: 2
Start Page Number: 220
End Page Number: 235
Publication Date: Jun 2013
Journal: Dynamic Games and Applications
Authors: ,
Keywords: pareto-optimality, stopping problem, Nash equilibrium
Abstract:

Multi‐person stopping games with players’ priorities are considered. Players observe sequentially offers Y 1,Y 2,… at jump times T 1,T 2,… of a Poisson process. Y 1,Y 2,… are independent identically distributed random variables. Each accepted offer Y n results in a reward G n =Y n r(T n ), where r is a non‐increasing discount function. If more than one player wants to accept an offer, then the player with the highest priority (the lowest ordering) gets the reward. We construct Nash equilibrium in the multi‐person stopping game using the solution of a multiple optimal stopping time problem with structure of rewards {G n }. We compare rewards and stopping times of the players in Nash equilibrium in the game with the optimal rewards and optimal stopping times in the multiple stopping time problem. It is also proved that presented Nash equilibrium is a Pareto optimum of the game. The game is a generalization of the Elfving stopping time problem to multi‐person stopping games with priorities.

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