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We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…
We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture…
This tutorial article puts forth a framework to analyze the noncooperative strategic interactions among the members of a large population of bounded rationality agents. Our approach hinges on, unifies and generalizes existing methods and…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this…
We report on new stability conditions for evolutionary dynamics in the context of population games. We adhere to the prevailing framework consisting of many agents, grouped into populations, that interact noncooperatively by selecting…
The prevailing methodology for analyzing population games and evolutionary dynamics in the large population limit assumes that a Poisson process (or clock) inherent to each agent determines when the agent can revise its strategy. Hence,…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
We establish Nash equilibrium learning in large populations of noncooperative, strategic agents. Our analysis considers the broadest class to date of payoff mechanisms with first-order modifications, capable of modeling bounded rationality…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's…
In this work, we consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is…
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…
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept…
Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
We consider a large population of learning agents noncooperatively selecting strategies from a common set, influencing the dynamics of an exogenous system (ES) we seek to stabilize at a desired equilibrium. Our approach is to design a…
In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on…
This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal…
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…