Discrete time stochastic multi-player competitive games with affine payoffs

A novel class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is examined. The affine 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 the so-called redistribution games were studied. We identify conditions under which optimal equilibria and value for a multi-player affine game exist. We also examine stochastic multi-period affine games and we show that, under mild assumptions, they can be solved by the method of backward induction.