Stochastic games with additive transitions

We deal with n-player AT stochastic games, where AT stands for additive transitions. These are stochastic games in which the transition probability vector ps(as), for action combination as=(as1,…,asn) in state s, can be decomposed into player-dependent components as:ps(as)=∑i=1nλsi·psi(asi),where λsi∈[0,1] for all players i  , and ∑i=1nλsi=1, and where psi(asi) is a probability distribution on the finite set of states S  . Here, λsi reflects the influence of player i on the transitions in state s. As such the class of AT stochastic games covers several other well-known classes such as perfect information stochastic games, stochastic games with switching control, and so-called ARAT stochastic games.With respect to the average reward it is not clear whether ε-equilibria always exist in general n-player stochastic games. For the class of n-player AT games we establish the existence of 0-equilibria, although the strategies involved may be history dependent. In addition we have the following results for the two-player case: (1) for zero-sum AT games, stationary 0-optimal strategies always exist; (2) for two-player general-sum AT absorbing games, there always exist stationary ε-equilibria, for all ε > 0.Several examples are provided to clarify the issues and to demonstrate the sharpness of the results.