In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...

Shapley’s discounted stochastic games, Everett’s recursive games and Gillette’s undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games. When the number of positions of the game is constant, our algorithms run in polynomial time.

Classes of two-person zero-sum games termed "equivalent games" are defined. These are games with identical value and identical optimal mixed-strategies but with different matrix entries and thus different opportunities for exploiting a nonrational opponent. An experiment was conducted to investigate the strategy-choice behavior of subjects playing pairs of these "equivalent games." Also investi...

We consider two-person zero-sum stochastic games with perfect information and, for each k ∈ Z+, introduce a new payoff function, called the k-total reward. For k = 0 and 1 they are the so called mean and total rewards, respectively. For all k, we prove solvability of the considered games in pure stationary strategies, and show that the uniformly optimal strategies for the discounted mean payoff...

We propose a connection between finite zero-sum stochastic games (henceforth games) and multiparameter eigenvalue problems. This connection, which relies on the theory developed by Shapley Snow for matrix games, opens new possibilities in study of games. In particular, we derive from this handful results

The Markov game (also called stochastic game (Filar & Vrieze 1997)) has been adopted as a theoretical framework for multiagent reinforcement learning (Littman 1994). In a Markov game, there are n agents, each facing a Markov decision process (MDP). All agents’ MDPs are correlated through their reward functions and the state transition function. As Markov decision process provides a theoretical ...

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen from a specified set. We show that it is NP-hard for the designer to decide whether she can make her choices so that no action in a given set gets played in e...

The set Gn of all n-person games 1 may be considered a convex subset of a euclidean space; Gn has dimension 2 n — n — 2. Although it has not been proved that all games possess a solution, large classes of solvable games have been discovered. In [2], Shapley defined a certain class of solvable games—the quota games—and showed that from the point of view of dimension, the set Qn of all ^-person q...

The solution is given here for the infinitely repeated two-person zero-sum,games of inr complete information characterized by 2 X 2 games, with information matrxces b for the ftrst game and( b ab)for the second game.

In strategic argumentation players exchange arguments to prove or reject a claim. This paper discusses and reports on research about two basic issues regarding the game-theoretic understanding of strategic argumentation games in the law: whether such games can be reasonably modelled as zero-sum games and as games with complete information.