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We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players'…
Formation strategy is one of the most important parts of many multi-agent systems with many applications in real world problems. In this paper, a framework for learning this task in a limited domain (restricted environment) is proposed. In…
Purpose: We propose a model to present a possible mechanism for obtaining sizeable behavioural structures by simulating an agent based on the evolutionary public good game with available social learning. Methods: The model considered a…
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network,…
We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
Game design hinges on understanding how static rules and content translate into dynamic player behavior - something modern generative systems that inspect only a game's code or assets struggle to capture. We present an automated design…
Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…
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…
Stochastic games are a popular framework for studying multi-agent reinforcement learning (MARL). Recent advances in MARL have focused primarily on games with finitely many states. In this work, we study multi-agent learning in stochastic…
We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…
We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy,…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…