Considerate Equilibrium

TL;DR

This paper introduces a new concept of considerate equilibrium in social network-based strategic games, proving its existence, providing an efficient algorithm for symmetric resource selection games, and analyzing its stability and convergence.

Contribution

It defines considerate equilibrium considering social network constraints and selfish behavior, proving its existence and providing an efficient computation method for symmetric resource selection games.

Findings

Existence of considerate equilibrium in all symmetric RSG with increasing delays.

Constructive proof and efficient algorithm for computing considerate equilibrium.

Considerate equilibrium also serves as a Nash equilibrium, ensuring stability against various behaviors.

Abstract

We consider the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent approach termed partition equilibrium. We assume that players in a strategic game are embedded in a social network, and there are coordination constraints that restrict the potential coalitions that can jointly deviate in the game to the set of cliques in the social network. In addition, players act in a "considerate" fashion to ignore potentially profitable (group) deviations if the change in their strategy may cause a decrease of utility to their neighbors. We study the properties of such considerate equilibria in application to the class of resource selection games (RSG). Our main result proves existence of a considerate equilibrium in all symmetric RSG with strictly increasing delays, for any social network among the players. The existence proof is constructive and yields an efficient algorithm. In fact, the computed considerate equilibrium is a Nash equilibrium for the standard RSG showing that there exists a state that is stable against selfish and considerate behavior simultaneously. In addition, we show results on convergence of considerate dynamics.