Stochastic Multi-player Competitive Games in Discrete Time

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.