DEWS Colloquia #9: Seeking Nash Equilibria under Nonconvex Coupling Constraints

In noncooperative games, a number of self-interested agents with individual dynamics and constraints aim at optimizing their objective functions, possibly in competition with each other, e.g. due to the scarcity of shared resources. Nash games represent the common way to define the solution of these games in many practical applications, from electricity markets to mobile-edge computing. From a control-theoretic perspective, the objective is to develop a coordination mechanism, namely, a discrete-time dynamical system for updating the strategies of the agents towards an equilibrium. This talk will focus on a class of Nash games with nonconvex coupling constraints where a novel notion of local equilibrium is defined leveraging on the theory of tangent cones. The stability properties of these equilibria as well as the conditions for their existence and uniqueness are presented and discussed. Two discrete-time distributed dynamics or fixed-point iterations are proposed to compute these equilibria, while the convergence is show under (strongly) monotone assumptions on the pseudo-gradient mapping of the game. Applications to energy demand management under power flow constraints are shown.

20.01.2023

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