On the logic of coalitional games

• Authors: Thomas Ågotnes;Wiebe van der Hoek;Michael Wooldridge
• Venue: AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
• Year: 2006

We develop a logic for representing and reasoning about coalitional games without transferable payoffs. Although a number of logics of cooperation have been proposed over the past decade (notably Coalition Logic [14] and Alternating-time Temporal Logic [1]), these logics focused primarily on the issue of strategic cooperative ability -- what states a coalition can effectively enforce - and have tended to ignore the essential issue of the preferences that agents have over such states; in addition, the connection between such logics and coalitional games, in the sense of cooperative game theory, is left implicit. The Coalitional Game Logic (CGL) that we develop in this paper differs from such previous logics in two important respects. First, CGL includes operators that make it directly possible to represent an agent's preferences over outcomes. Second, we interpret formulae of CGL directly with respect to coalitional games without transferable payoff, thereby establishing an explicit link between formulae of the logic and properties of coalitional games. We show that these coalitional games cannot be seen directly as models for Coalition Logic. We give a complete axiomatization of CGL, prove that it is expressively complete with respect to coalitional games without transferable payoff, show that the satisfiability problem for the logic is NP-complete, and to illustrate its use, we show how the logic can be used to characterise axiomatically a number of well-known solution concepts for coalitional games, including for example non-emptiness of the core.