Locally-Aware Constrained Games on Networks

TL;DR

This paper introduces a framework for constrained network games where players are only aware of local constraints, analyzing how awareness levels influence equilibrium solutions and transforming the problem into a dual unconstrained game.

Contribution

It defines locally-aware constrained games, characterizes their equilibria, and introduces a dual game approach to simplify analysis, with case studies on linear quadratic games.

Findings

Higher awareness levels expand the set of equilibria.

Duality allows converting constrained games into unconstrained two-layer games.

Linear quadratic case studies validate the theoretical results.

Abstract

Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyber-physical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints. To this end, this paper proposes a game framework to study constrained games on networks, where the players are locally aware of the constraints. We use \textit{awareness levels} to capture the scope of the network constraints that players are aware of. We first define and show the existence of generalized Nash equilibria (GNE) of the game, and point out that higher awareness levels of the players would lead to a larger set of GNE solutions. We use necessary and sufficient conditions to characterize the GNE, and propose the concept of the dual game to show that one can convert a locally-aware constrained game into a two-layer unconstrained game problem. We use linear quadratic games as case studies to corroborate the analytical results, and in particular, show the duality between Bertrand games and Cournot games.%, where each layer comprises an unconstrained game.