Stochastic Multi-player Competitive Games in Discrete Time

Ivan Guo; Marek Rutkowski

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arXiv · 1405.2716

Stochastic Multi-player Competitive Games in Discrete Time

Ivan Guo·Marek Rutkowski

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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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Ivan Guo, Marek Rutkowski. 2014-05-12. Stochastic Multi-player Competitive Games in Discrete Time. https://arxiv.org/abs/1405.2716

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