Iterative algorithms such as Counterfactual Regret Minimization (CFR) are the most popular way to solve large zero-sum imperfect-information games. In this paper we introduce Best-Response Pruning (BRP), an improvement to iterative algorithms such as CFR that allows poorly-performing actions to be temporarily pruned. We prove that when using CFR in zero-sum games, adding BRP will asymptotically...

Boolean games, introduced by [15, 14], allow for expressing compactly two-players zero-sum static games with binary preferences: an agent’s strategy consists of a truth assignment of the propositional variables she controls, and a player’s preferences is expressed by a plain propositional formula. These restrictions (two-players, zero-sum, binary preferences) strongly limit the expressivity of ...

In two-player zero-sum games, if both players minimize their average external regret, then the average of the strategy profiles converges to a Nash equilibrium. For n-player general-sum games, however, theoretical guarantees for regret minimization are less understood. Nonetheless, Counterfactual Regret Minimization (CFR), a popular regret minimization algorithm for extensiveform games, has gen...

Non-cooperative decision-making problems in a decentralized supply chain can be characterized and studied using a stochastic game model. In an earlier paper, the authors developed a methodology that uses machine learning for finding (near) optimal policies for non-zero sum stochastic games, and applied their methodology on an N-retailer and W-warehouse inventory-planning problem. The focus of t...

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform value, generalizing several results of the literature. A preliminary existence result is obtained for a certain class of stochastic games played with pure strate...

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.

The interchangeability property of Nash equilibria in two-player zerosum games is well-known. This paper studies possible generalizations of this property to multi-party zero-sum games. A form of interchangeability property for strict Nash equilibria in such games is established. It is also shown, by proving a completeness theorem, that strict Nash equilibria do not satisfy any other non-trivia...