Coalitional Games with Stochastic Characteristic Functions and Private Types

The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in advance. This paper studies a new setting (a task allocation problem) where the characteristic function is not known and it is controlled by some private information from the players. Hence, the challenge here is twofold: (i) incentivize players to reveal their private information truthfully, (ii) incentivize them to collaborate together. We show that existing reward distribution mechanisms or auctions cannot solve the challenge. Hence, we propose the very first mechanism for the problem from the perspective of both mechanism design and coalitional games.