Approximate Core Allocation for Large Cooperative Security Games

Abstract

Coalition games have been recently used for modeling a variety of security problems. From securing the wireless transmissions in decentralized networks to employing effective intrusion detection systems in large organizations, cooperation among interested parties has shown to bring significant benefits. Motivating parties to abide to a solution is, however, a key problem in bridging the gap between theoretical models and practical solutions. Benefits should be distributed among players (wireless nodes in a network, different divisions of an organization in security risk management, or organizations cooperating to fight spam), such that no group of players is motivated to break off and form a new coalition. This problem, referred to as core allocation, grows computationally very expensive with a large number of agents. In this paper, we present a novel approximate core allocation algorithm, called the bounding boxed core (BBC), for large cooperative security games in characteristic form that rely on superadditivity. The proposed algorithm is an anytime (an algorithm is called anytime if it can be interrupted at any time point during execution to return an answer whose value, at least in certain classes of stochastic processes, improves in expectation as a function of the computation time) algorithm based on iterative state space search for better solutions. Experimental results on a 25-player game, with roughly 34 million coalitions, show that BBC shrinks the 25-dimensional bounding-box to times its initial hypervolume.