07431 Abstracts Collection -- Computational Issues in Social Choice

From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431 on ``Computational Issues in Social Choice\u27\u27 was held at the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their recent research, and ongoing work and open problems were discussed. The abstracts of the talks given during the seminar are collected in this paper. The first section summarises the seminar topics and goals in general. Links to full papers are provided where available

ABSTRACT On the Logic of Coalitional Games

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

ABSTRACT On the Logic of Coalitional Games

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

ABSTRACT On the Logic of Coalitional Games

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