A class of stochastic positional games which extend the cyclic games and Markov decision problems with average and discounted optimization costs criteria is formulated and studied. Nash equilibria conditions for considered class of stochastic positional games are derived and some approaches for determining Nash equilibria are described.

The paradigm of randomly-furcating stochastic differential games incorporates additional stochastic elements via randomly branching payoffs in stochastic differential games. This paper considers dynamically stable cooperative solutions in randomly furcating stochastic differential games. Analytically tractable payoff distribution procedures contingent upon specific random realizations of the st...

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...

Introduction.-In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players. We shall assume a finite number, N, of positions, and finite numbers Mk, nk of choices at each position; nevertheless, the game may not be bounded in length. If, when at position k, the players choose their ith and jth alternatives...

In 1953, Lloyd Shapley contributed his paper "Stochastic games" to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley's contribution.

A stochastic graph game is played by two-players on a game graph with probabilistic transitions. We present a strategy improvement algorithm for stochastic graph games with ω-regular conditions specified as parity objectives. From the strategy improvement algorithm we obtain a randomized sub-exponential time algorithm to solve stochastic parity games.

Congestion games ignore the stochastic nature of resource delays and the risk-averse attitude of the players to uncertainty. To take these aspects into account, we introduce two variants of atomic congestion games, one with stochastic players, where each player assigns load to her strategy independently with a given probability, and another with stochastic edges, where the latency functions are...

Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for general-sum stochastic games by Filar and Vrieze [2004]. However, the optimization problem there has a non-linear objective and non-linear constraints with special s...

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak convergence for probabilistic processes) towards their mean-field limit, i.e an ordinary differential equation (ODE) in the general case. We focus then on a cla...