Coalitional Games with Stochastic Characteristic Functions and Private Types

TL;DR

This paper introduces a novel mechanism for coalitional games where players have private information and the characteristic function is unknown, addressing incentive issues in both truthfulness and collaboration.

Contribution

It proposes the first mechanism combining mechanism design and coalitional game theory for unknown, private characteristic functions in task allocation.

Findings

First mechanism for private, unknown characteristic functions

Addresses incentive compatibility for truthfulness and collaboration

Bridges mechanism design with coalitional game theory

Abstract

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.