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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…
In Part I \cite{Zhao13TSPasync1}, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We…
This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case…
We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics (Hart 2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly "best…
Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are…
Decision-making individuals often imitate their highest-earning fellows rather than optimize their own utilities, due to bounded rationality and incomplete information. Perpetual fluctuations between decisions have been reported as the…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
Machine learning is now ubiquitous in societal decision-making, for example in evaluating job candidates or loan applications, and it is increasingly important to take into account how classified agents will react to the learning…
A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner's…
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
Models in evolutionary game theory traditionally assume symmetric interactions in homogeneous environments. Here, we consider populations evolving in a heterogeneous environment, which consists of patches of different qualities that are…
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…
Noncooperative games with uncertain payoffs have been classically studied under the expected-utility theory framework, which relies on the strong assumption that agents behave rationally. However, simple experiments on human decision makers…
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we…
This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…
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…
We analyze a simple model of adaptive competition which captures essential features of a variety of adaptive competitive systems in the social and biological sciences. Each of N agents, at each time step of a game, joins one of two groups.…