Related papers: Analysis of a Finite State Many Player Game Using …
In this paper, we consider both finite and infinite horizon discounted dynamic mean-field games where there is a large population of homogeneous players sequentially making strategic decisions and each player is affected by other players…
Mean-payoff games are important quantitative models for open reactive systems. They have been widely studied as games of full observation. In this paper we investigate the algorithmic properties of several sub-classes of mean-payoff games…
We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players.…
We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, for the case where the players are restricted to finite-memory strategies. First, we describe a general framework, where…
A recent paper by Bhatia, Chin, Mani, and Mossel (2026) defined stochastic processes aimed at modeling the game of War for {\em two players} with $n$ cards. That paper showed that these models, assuming uniform random decks, are equivalent…
We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…
This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…
Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces is a long standing open…
We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants…
We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be…
We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…
Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a…
We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino.…