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=1n λsi · psi(asi), where λsi ∈ [0,1] for all players i, and ∑i=1n λsi = 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>O.
