Related papers: On Nash Equilibria in Play-Once and Terminal Deter…
We consider sequences of games $\mathcal{G}=\{G_1,G_2,\ldots\}$ where, for all $n$, $G_n$ has the same set of players. Such sequences arise in the analysis of running time of players in games, in electronic money systems such as Bitcoin and…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
Finite-horizon linear quadratic (LQ) games admit a unique Nash equilibrium, while infinite-horizon settings may have multiple. We clarify the relationship between these two cases by interpreting the finite-horizon equilibrium as a nonlinear…
This work addresses the issue of the convergence of an $N$-player game towards a limit model involving a continuum of players, as the number of agents $N$ goes to infinity. More precisely, we investigate the convergence of Nash equilibria…
Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…
We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to…
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…
We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash…
We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…
Recently, a new model extending the standard replicator equation to a finite set of players connected on an arbitrary graph was developed in evolutionary game dynamics. The players are interpreted as subpopulations of multipopulations…
We introduce and investigate certain $N$ player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium. Most significantly, we find that the universal local limit of the equilibrium is sensitive to…
We consider a partially asymmetric multi-players zero-sum game with two strategic variables. All but one players have the same payoff functions, and one player (Player $n$) does not. Two strategic variables are $t_i$'s and $s_i$'s for each…
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…
A Linear Quadratic Deterministic Continuous Time Game with many symmetric players is considered and the Linear Feedback Nash strategies are studied as the number of players goes to infinity. We show that under some conditions the limit of…