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Efficient best response computation for strategic network formation under attack. (English) Zbl 1403.91067
Bilò, Vittorio (ed.) et al., Algorithmic game theory. 10th international symposium, SAGT 2017, L’Aquila, Italy, September 12–14, 2017. Proceedings. Cham: Springer (ISBN 978-3-319-66699-0/pbk; 978-3-319-66700-3/ebook). Lecture Notes in Computer Science 10504, 199-211 (2017).
Summary: 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 S. Goyal et al. [Lect. Notes Comput. Sci. 10123, 429–443 (2016; Zbl 1404.91055)] 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 through the network via neighboring nodes.
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.
For the entire collection see [Zbl 1371.91003].

MSC:
91A43 Games involving graphs
91A22 Evolutionary games
90B10 Deterministic network models in operations research
91-04 Software, source code, etc. for problems pertaining to game theory, economics, and finance
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