Stochastic games on a product state space:
the periodic case
János Flesch · Gijs Schoenmakers · Koos Vrieze
Accepted: 29 January 2009
Abstract
We examine so-called product-games. These are n-player stochastic
games played on a product state space S1 × · · · × Sn, in which player i controls
the transitions on Si . For the general n-player case, we establish the existence of
0-equilibria. In addition, for the case of two-player zero-sum games of this type, we
show that both players have stationary 0-optimal strategies. In the analysis of productgames,
interestingly, a central role is played by the periodic features of the transition
structure. Flesch et al. (Math Oper Res 33, 403–420, 2008) showed the existence of
0-equilibria under the assumption that, for every player i , the transition structure on
Si is aperiodic. In this article, we examine product-games with periodic transition
structures. Even though a large part of the approach in Flesch et al. (Math Oper Res
33, 403–420, 2008) remains applicable, we encounter a number of tricky problems
that we have to address.We provide illustrative examples to clarify the essence of the
difference between the aperiodic and periodic cases.