Nash and Wardrop equilibria in aggregative games with coupling constraints

We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibrium. By exploiting a characterization of the two equilibria as solutions of variational inequalities, we bound their distance with a decreasing function of the population size. As second contribution, we propose two decentralized algorithms that converge to such equilibria and are capable of coping with constraints coupling the strategies of different agents. Finally, we study the applications of charging of electric vehicles and of route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The first three authors contributed equall

Genetic algorithm for closed-loop equilibrium of high-order linear-quadratic dynamic games

Cataloged from PDF version of article.In this paper, we implement an adaptive search algorithm, genetic algorithm to derive closed-loop Nash equilibria for linear-quadratic dynamic games. The computation of these equilibria is quite difficult to deal with analytically and numerically. Our strategy is to search over all rime-invariant strategies depending only on the current value of the state. Also provided are some evidences which show the success of the algorithm. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved

Generalized Stochastic Dynamic Aggregative Game for Demand-Side Management in Microgrids with Shared Battery

In this paper, we focus on modeling and analysis of demand-side management in a microgrid where agents utilize grid energy and a shared battery charged by renewable energy sources. We model the problem as a generalized stochastic dynamic aggregative game with chance constraints that capture the effects of uncertainties in the renewable generation and agents' demands. Computing the solution of the game is a complex task due to probabilistic and coupling constraints among the agents through the state of charge of the shared battery. We investigate the Nash equilibrium of this game under uncertainty considering both the uniqueness of the solution and the effect of uncertainty on the solution. Simulation results demonstrate that the presented stochastic method is superior to deterministic methods

Evolutionary Game Theory Squared: Evolving Agents in Endogenously Evolving Zero-Sum Games

The predominant paradigm in evolutionary game theory and more generally online learning in games is based on a clear distinction between a population of dynamic agents that interact given a fixed, static game. In this paper, we move away from the artificial divide between dynamic agents and static games, to introduce and analyze a large class of competitive settings where both the agents and the games they play evolve strategically over time. We focus on arguably the most archetypal game-theoretic setting -- zero-sum games (as well as network generalizations) -- and the most studied evolutionary learning dynamic -- replicator, the continuous-time analogue of multiplicative weights. Populations of agents compete against each other in a zero-sum competition that itself evolves adversarially to the current population mixture. Remarkably, despite the chaotic coevolution of agents and games, we prove that the system exhibits a number of regularities. First, the system has conservation laws of an information-theoretic flavor that couple the behavior of all agents and games. Secondly, the system is Poincar\'{e} recurrent, with effectively all possible initializations of agents and games lying on recurrent orbits that come arbitrarily close to their initial conditions infinitely often. Thirdly, the time-average agent behavior and utility converge to the Nash equilibrium values of the time-average game. Finally, we provide a polynomial time algorithm to efficiently predict this time-average behavior for any such coevolving network game.Comment: To appear in AAAI 202