The Core of Uncertain Coalitional Game Based on Hurwicz Criterion with Application to Cyber Security Information Sharing

Abstract

The coalitional game focuses on how people share the payoffs of collaboration when they form coalitions. However, we cannot accurately obtain the different coalitions’ payoffs because of the actual situation’s limitation or economic and technical factors. Therefore, we have to rely on experts in the field to estimate the likelihood of various events and give their belief degrees. To deal with the belief degrees, scholars of uncertainty theory suppose the transferable payoffs to be uncertain variables and propose the uncertain coalitional game. Many expected and optimistic solution concepts have been put forward in the literature, even though the expected value criterion does not consider the decision-maker’s attitude to risk, and the optimistic value criterion is too extreme. To better describe the different subjective judgments of decision-makers, the Hurwicz criterion is applied to the uncertain coalitional game, in which the players intend to maximize their Hurwicz payoffs. Besides, the method to discover the Hurwicz-core is provided, and the condition that the core is nonempty is proved. What’s more, the Hurwicz–Shapley value is mathematically proven to be in the Hurwicz-core in a convex uncertain coalitional game. An application in cyber security information sharing is provided.