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In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed…
This paper presents a learning dynamic with almost sure convergence guarantee for any stochastic game with turn-based controllers (on state transitions) as long as stage-payoffs induce a zero-sum or identical-interest game. Stage-payoffs…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The…
In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called $\mathcal…
A zero-sum two person Perfect Information Stochastic game (PISG) under limiting average payoff has a value and both the maximiser and the minimiser have optimal pure stationary strategies. Firstly we form the matrix of undiscounted payoffs…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…
We study agents competing against each other in a repeated network zero-sum game while applying the multiplicative weights update (MWU) algorithm with fixed learning rates. In our implementation, agents select their strategies…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
In this paper, a new method is proposed to compute the rolling Nash equilibrium of the time-invariant nonlinear two-person zero-sum differential games. The idea is to discretize the time to transform a differential game into a sequential…
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…
We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games to a concurrent setting where the two players choose moves simultaneously and independently at each state. For…