Summary: Noname manuscript No.
(will be inserted by the editor)
Strategic Multiway Cut and Multicut Games
Elliot Anshelevich · Bugra Caskurlu · Ameya Hate
Abstract We consider cut games where players want to cut themselves off from different parts of a network.
These games arise when players want to secure themselves from areas of potential infection. For the game-
theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium
as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a
2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding
exact and approximate equilibria in these games.
Keywords Network Formation Games · Price of Stability · Approximate Nash Equilibrium · Multiway
Cut · Multi-cut
1 Introduction and Model
Networked systems for transport, communication, and social interaction have contributed to all aspects of
life by increasing economic and social efficiency. However, increased connectivity also gives intruders and
attackers better opportunities to maliciously spread in the network, whether the spread is of disinformation,
or of contamination in the water supply . Anyone participating in a networked system may therefore desire
to undertake appropriate security measures in order to protect themselves from such malicious influences.
We introduce a Network Cutting Game, which is a game-theoretic framework where a group of self-