Efficient Best-Response Computation for Strategic Network Formation under Attack

TL;DR

This paper presents an efficient algorithm for computing best-response strategies in a realistic network formation game under attack, addressing computational intractability issues in prior models and enabling practical equilibrium analysis.

Contribution

It introduces a tractable model for strategic network formation under attack and provides the first efficient algorithm for best-response computation in this setting.

Findings

The model is both realistic and computationally tractable.

An efficient algorithm for best-response computation is developed.

Deciding Nash equilibrium existence can be done efficiently.

Abstract

Inspired by real world examples, e.g. the Internet, researchers have introduced an abundance of strategic games to study natural phenomena in networks. Unfortunately, almost all of these games have the conceptual drawback of being computationally intractable, i.e. computing a best response strategy or checking if an equilibrium is reached is NP-hard. Thus, a main challenge in the field is to find tractable realistic network formation models. We address this challenge by investigating a very recently introduced model by Goyal et al. [WINE'16] which focuses on robust networks in the presence of a strong adversary who attacks (and kills) nodes in the network and lets this attack spread virus-like to neighboring nodes and their neighbors. Our main result is to establish that this natural model is one of the few exceptions which are both realistic and computationally tractable. In particular, we answer an open question of Goyal et al. by providing an efficient algorithm for computing a best response strategy, which implies that deciding whether the game has reached a Nash equilibrium can be done efficiently as well. Our algorithm essentially solves the problem of computing a minimal connection to a network which maximizes the reachability while hedging against severe attacks on the network infrastructure and may thus be of independent interest.