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Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
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 mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…
This paper integrates the studies of various countries' behaviors, e.g., waging wars and entering into military alliances, into a general framework of \emph{countries' relation formation}, which consists of two components, i.e., a static…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…
We consider a dynamic version of sender-receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium…
This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…
Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
We propose a decentralized game-theoretic framework for dynamic task allocation problems for multi-agent systems. In our problem formulation, the agents' utilities depend on both the rewards and the costs associated with the successful…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
The paper is concerned with the feedback approach to the deterministic mean field type differential games. Previously, it was shown that suboptimal strategies in the mean field type differential game can constructed based on functions of…
We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…