Connected Subgraph Defense Games

Abstract We study a security game over network played between defender and k attackers . Every attacker chooses, probabilistically, node of the to damage. The probabilistically as well, connected induced subgraph $$\lambda $$ λ nodes scan clean. Each wishes maximize probability escaping her cleaning by defender. On other hand, goal is expected number that she catches. This generalization model from seminal paper Mavronicolas et al. (in: International symposium on mathematical foundations computer science, MFCS, pp 717–728, 2006). are interested in Nash equilibria this game, well characterizing defense-optimal networks which allow for best equilibrium defense ratio ; catches equilibrium. provide characterization networks. characterizations us show even if centrally controlled remain same. In addition, we give an algorithm computing equilibria. Our requires exponential time worst case, but it polynomial-time constantly close 1 or n For special case tree-networks, further refine our allows derive deciding whether tree computes prove $${\mathtt {NP}}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">NP -hard find best-defense strategy not defense-optimal. complement negative result with constant-approximation solutions optimal ones general graphs. Finally, asymptotically (almost) tight bounds Price Defense any all