Near-Strong Equilibria in Network Creation Games

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Abstract

We introduce a new solution concept for games, near-strong equilibrium, a variation of strong equilibrium. Previous work has shown the existence of 2-strong pure strategy equilibrium for network creation games with 1 < α< 2 and that k-strong equilibrium for k ≥ 3 does not exist. In this paper we show that 3-near-strong equilibrium exists, and provide tight bounds on existence of k-near-strong equilibria for k ≥ 4. Then we repeat our analysis for correlated mixed strategies, where we show that, surprisingly, 3-correlated-strong equilibrium exists, and also show bounds for existence of correlated k-strong equilibria. Moreover, the equilibrium profile can be arbitrarily close to the social optimum. For both pure and correlated settings, we show examples where no equilibrium exists. On the conceptual level, our work contributes to the recent literature of extensions of strong equilibrium, while providing positive results for stability against group deviations in one of the basic settings discussed in the algorithmic game theory literature.