The Generalized Stackelberg Equilibrium of the Two-Person Stopping Game

Abstract

AbstractIn modeling the bilateral selection of states of the process, Dynkin (Dokl Akad Nauk USSR 185:241–288, 1969) proposed a two-person game in which players use stopping moments as strategies. The purpose of this work is to present a model of the game in which the players have different information about the process itself, as well as various laws to stop the process and accept its state. The game model uses the stochastic process apparatus, in particular, the ability to create different filters for the same process. The sets of stopping moments based on different filters are not identical, which allows us to model different sets of strategies for players. We show that the follower, by observing the behavior of a rational leader, can recover information that is lost due to the lack of complete observation of the state of the process. In the competition of two opponents for the maximum of the i.i.d. sequence, one of whom has access to full information and the other only knows their relative ranks, we found the generalized Stackelberg equilibrium. If the priority of a player observing the relative ranks is less than 50%, then that player modifies his strategy based on the behavior of the second player. For a player with full information, information about the behavior of the player observing the relative ranks is useless.