Strategic Network Formation under Attack

Master Project - Summer 2016

Supervisors: Prof. Dr. Tobias Friedrich, Dr. Pascal Lenzner
Link: Courses IT-Systems Engineering

In this Master Project we set out to investigate such a game-theoretic model both theoretically and experimentally. In our strategic network formation game there are players which can create costly links to other players. The combination of the individual decisions of all players then induces a network. The goal of each player is to obtain a reliable network, which ensures good connectivity to all other players. However, players are greedy and thus weigh their individually obtained network quality against the cost spent for creating links. But if everyone tries to free-ride the network, what happens to the overall network quality?

Network before attack Network after attack

We are especially interested in networks, which are reliable even under attack from a malicious third party. Even worse, we assume that an attacked node of the network completely fails and the attack spreads virus-like to its neighbors. However, there is hope for our players: they can selfishly decide to buy a firewall and thus protect themselves.

Results

The results of the project have resulted in the following publications:

Friedrich, Tobias; Ihde, Sven; Keßler, Christoph; Lenzner, Pascal; Neubert, Stefan; Schumann, David Efficient Best Response Computation for Strategic Network Formation under Attack. Symposium on Algorithmic Game Theory (SAGT) 2017: 199-211

[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]

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.

@inproceedings{friedrich2017efficient, 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.}, author = {Friedrich, Tobias and Ihde, Sven and Keßler, Christoph and Lenzner, Pascal and Neubert, Stefan and Schumann, David}, booktitle = {Symposium on Algorithmic Game Theory (SAGT)}, keywords = {svenihde year2017 christophkessler tobiasfriedrich davidschumann pascallenzner stefanneubert sagt}, pages = {199-211}, title = {Efficient Best Response Computation for Strategic Network Formation under Attack}, year = 2017 }
Friedrich, Tobias; Ihde, Sven; Keßler, Christoph; Lenzner, Pascal; Neubert, Stefan; Schumann, David Brief Announcement: Efficient Best Response Computation for Strategic Network Formation under Attack. Symposium on Parallelism in Algorithms and Architectures (SPAA) 2017: 321-323

[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]

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 establishing that the recently introduced model by Goyal et al.[WINE'16], which focuses on robust networks in the presence of a strong adversary, is a rare exception which is both realistic and computationally tractable. In particular, we sketch 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.

@inproceedings{friedrich2017brief, 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 establishing that the recently introduced model by Goyal et al.[WINE'16], which focuses on robust networks in the presence of a strong adversary, is a rare exception which is both realistic and computationally tractable. In particular, we sketch 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.}, address = {New York, NY, USA}, author = {Friedrich, Tobias and Ihde, Sven and Keßler, Christoph and Lenzner, Pascal and Neubert, Stefan and Schumann, David}, booktitle = {Symposium on Parallelism in Algorithms and Architectures (SPAA)}, keywords = {svenihde year2017 christophkessler spaa tobiasfriedrich davidschumann pascallenzner stefanneubert}, pages = {321-323}, publisher = {ACM}, title = {Brief Announcement: Efficient Best Response Computation for Strategic Network Formation under Attack}, year = 2017 }