Related papers: Evolutionary Dynamics in Continuous-time Finite-st…
Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. In such games, agents maximize their utility by choosing actions that differ from their neighbors'…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
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…
We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
This paper presents a model of network formation in repeated games where the players adapt their strategies and network ties simultaneously using a simple reinforcement-learning scheme. It is demonstrated that the coevolutionary dynamics of…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…
Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
The Inspection Game is the canonical model for the strategic conflict between law enforcement (inspectors) and citizens (potential criminals). Its classical Mixed-Strategy Nash Equilibrium (MSNE) is afflicted by a paradox: the equilibrium…
The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…
We consider both discrete and continuous time finite state-action stochastic games. In discrete time stochastic games, it is known that a stationary Blackwell-Nash equilibrium (BNE) exists for a single controller additive reward (SC-AR)…
We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues,…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
Mean field game facilitates analyzing multi-armed bandit (MAB) for a large number of agents by approximating their interactions with an average effect. Existing mean field models for multi-agent MAB mostly assume a binary reward function,…
We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run behavior of stochastic dynamics of many…
We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…
We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic dynamics of spatial games with multiple…
We introduce Mean Field Markov games with $N$ players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the…