We consider some well known families of two-player, zero-sum, turn-based, perfect information games that can be viewed as specical cases of Shapley’s stochastic games. We show that the following tasks are polynomial time equivalent: • Solving simple stochastic games, • solving stochastic mean-payoff games with rewards and probabilities given in unary, and • solving stochastic mean-payoff games ...

We consider two-players zero-sum perfect information stochastic games with finitely many states and actions and examine the problem of existence of pure stationary optimal strategies. We show that the existence of such strategies for one-player games (Markov decision processes) implies the existence of such strategies for two-player games. The result is general and holds for any payoff mapping.

We present a relatively general model of repeated games first, which will be later specialized for each different repeated game with different monitoring structure. Stage game is a standard strategic (normal) form game G = {N,A, g} , where N = {1, 2, ..., n} be the set of players, Ai is player i’s finite or compact action set ¡ A = Q i∈N Ai ¢ , and g : A→ <n is the payoff functions of n players...

We present a general construction for eliminating imperfect information from games with several players who coordinate against nature, and to transform them into two-player games with perfect information while preserving winning strategy profiles. The construction yields an infinite game tree with epistemic models associated to nodes. To obtain a more succinct representation, we define an abstr...

In nite perfect information extensive (FPIE) games, backward induction (BI) gives rise to all pure-strategy subgame perfect Nash equilibria, and iterative elimination of weakly dominated strategies (IEWDS) may give di erent outcomes for di erent orders of elimination. Duggan recently posed several conjectures in an e ort to better understand the relationship between BI and IEWDS in FPIE games. ...

We consider two-player games of perfect information of length some cardinal κ. It is well-known that for κ ≥ ω1 the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of κ under DCκ-the axiom of dependent choices generalized to κ. We generalize the notions of perfect and meager sets and provide characterizations with some s...