Network Creation Games: Think Global - Act Local

TL;DR

This paper introduces a new local view model for network creation games where agents optimize strategies within limited knowledge, analyzing its impact on computational complexity, equilibrium convergence, and network efficiency.

Contribution

It proposes a more optimistic locality model for network formation games, examining its effects on computational hardness, equilibrium quality, and strategy strength compared to previous worst-case locality models.

Findings

Locality affects the complexity of computing best responses.

Equilibrium convergence is influenced by local knowledge constraints.

The model maintains a non-constant lower bound on the price of anarchy.

Abstract

We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bil\`o et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy-changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the price of anarchy.