Stochastic Multi-player Competitive Games in Discrete Time
Ivan Guo, Marek Rutkowski

TL;DR
This paper introduces a new class of multi-player stochastic games with affine payoff redistribution, extending classic stopping games, and provides conditions for equilibrium existence and solution methods for multi-period cases.
Contribution
It proposes a novel class of multi-player stochastic games with affine payoff redistribution and extends existing results to multi-period stochastic affine games.
Findings
Existence conditions for optimal equilibria and game values.
Backward induction method for solving multi-period affine games.
Extension of classic two-player stopping game results.
Abstract
A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person stochastic stopping games introduced by Dynkin (1969). We first extend to the case of a single-period deterministic affine game the results from Guo and Rutkowski (2012,2014) where a particular subclass of competitive stopping games was studied. We identify conditions under which optimal equilibria and value for a multi-player competitive game with affine redistribution of payoffs exist. We also examine stochastic multi-period affine games and we show that, under mild assumptions, they can be solved by the backward induction.
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Taxonomy
TopicsEconomic theories and models · Auction Theory and Applications · Stochastic processes and financial applications
