Generalized Nash Equilibrium Seeking in Population Games under the Brown-von Neumann-Nash Dynamics

This paper investigates the problem of generalized Nash equilibrium (GNE) seeking in population games under the Brown-von Neumann-Nash dynamics and subject to general affine equality constraints. In particular, we consider that the payoffs perceived by the decision-making agents are provided by a so-called payoff dynamics model (PDM), and we show that an appropriate PDM effectively steers the agents to a GNE. More formally, using Lyapunov stability theory, we provide sufficient conditions to guarantee the asymptotic stability of the set of generalized Nash equilibria of the game, for the case when the game is a so-called stable game (also known as con-tractive game). Furthermore, we illustrate the application of the considered framework to an energy market game considering coupled equality constraints over the players decisions.

[1]  Sergio Grammatico,et al.  Continuous-Time Integral Dynamics for a Class of Aggregative Games With Coupling Constraints , 2020, IEEE Transactions on Automatic Control.

[2]  Shinkyu Park,et al.  From Population Games to Payoff Dynamics Models: A Passivity-Based Approac , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[3]  Qiuwei Wu,et al.  Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games in Prosumers , 2019, IEEE Transactions on Power Systems.

[4]  Sergio Grammatico,et al.  Distributed Generalized Nash Equilibrium Seeking in Aggregative Games on Time-Varying Networks , 2019, IEEE Transactions on Automatic Control.

[5]  Lacra Pavel,et al.  An operator splitting approach for distributed generalized Nash equilibria computation , 2019, Autom..

[6]  Hamidou Tembine,et al.  Constrained evolutionary games by using a mixture of imitation dynamics , 2018, Autom..

[7]  Deepa Kundur,et al.  Resilient Distributed Real-Time Demand Response via Population Games , 2017, IEEE Transactions on Smart Grid.

[8]  Lacra Pavel,et al.  A population game approach for dynamic resource allocation problems , 2017, Int. J. Control.

[9]  Maryam Kamgarpour,et al.  Learning Generalized Nash Equilibria in a Class of Convex Games , 2017, IEEE Transactions on Automatic Control.

[10]  Sergio Grammatico.  Dynamic Control of Agents Playing Aggregative Games With Coupling Constraints , 2016, IEEE Transactions on Automatic Control.

[11]  Nicanor Quijano,et al.  Constrained distributed optimization: A population dynamics approach , 2016, Autom..

[12]  William H. Sandholm,et al.  Population Games And Evolutionary Dynamics , 2010, Economic learning and social evolution.

[13]  Josef Hofbauer,et al.  Stable games and their dynamics , 2009, J. Econ. Theory.

[14]  Andreas Fischer,et al.  On generalized Nash games and variational inequalities , 2007, Oper. Res. Lett..

[15]  William H. Sandholm,et al.  Excess payoff dynamics and other well-behaved evolutionary dynamics , 2005, J. Econ. Theory.

[16]  Michael J. Smith,et al.  The Stability of a Dynamic Model of Traffic Assignment - An Application of a Method of Lyapunov , 1984, Transp. Sci..

[17]  J. Neumann,et al.  SOLUTIONS OF GAMES BY DIFFERENTIAL EQUATIONS , 1950 .

[18]  C. Ocampo‐Martinez,et al.  A Payoff Dynamics Model for Equality-Constrained Population Games , 2022, IEEE Control Systems Letters.

[19]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[20]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .