Related papers: A stability property in mean field type differenti…

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…

In this paper, we establish a large deviations principle (LDP) for interacting particle systems that arise from state and action dynamics of discrete-time mean-field games under the equilibrium policy of the infinite-population limit. The…

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…

We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding…

We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…

We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…

We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…

We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…

We consider infinite-state turn-based stochastic games of two players, Box and Diamond, who aim at maximizing and minimizing the expected total reward accumulated along a run, respectively. Since the total accumulated reward is unbounded,…