A Logic-Based Representation for Coalitional Games with Externalities

We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other co-existing coalitions. Although externalities play a key role in many real-life situations, very little attention has been given to this issue in the multi-agent system literature, especially with regard to the computational aspects involved. To this end, we propose a new representation which, in the spirit of Ieong and Shoham [9], is based on Boolean expressions. The idea behind our representation is to construct much richer expressions that allow for capturing externalities induced upon coalitions. We show that the new representation is fully expressive, at least as concise as the conventional partition function game representation and, for many games, exponentially more concise. We evaluate the efficiency of our new representation by considering the problem of computing the Extended and Generalized Shapley value, a powerful extension of the conventional Shapley value to games with externalities. We show that by using our new representation, the Extended and Generalized Shapley value, which has not been studied in the computer science literature to date, can be computed in time linear in the size of the input

Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input

Study of a Dynamic Cooperative Trading Queue Routing Control Scheme for Freeways and Facilities with Parallel Queues

This article explores the coalitional stability of a new cooperative control policy for freeways and parallel queuing facilities with multiple servers. Based on predicted future delays per queue or lane, a VOT-heterogeneous population of agents can agree to switch lanes or queues and transfer payments to each other in order to minimize the total cost of the incoming platoon. The strategic interaction is captured by an n-level Stackelberg model with coalitions, while the cooperative structure is formulated as a partition function game (PFG). The stability concept explored is the strong-core for PFGs which we found appropiate given the nature of the problem. This concept ensures that the efficient allocation is individually rational and coalitionally stable. We analyze this control mechanism for two settings: a static vertical queue and a dynamic horizontal queue. For the former, we first characterize the properties of the underlying cooperative game. Our simulation results suggest that the setting is always strong-core stable. For the latter, we propose a new relaxation program for the strong-core concept. Our simulation results on a freeway bottleneck with constant outflow using Newell's car-following model show the imputations to be generally strong-core stable and the coalitional instabilities to remain small with regard to users' costs.Comment: 3 figures. Presented at Annual Meeting Transportation Research Board 2018, Washington DC. Proof of conjecture 1 pendin

Coalitional Approaches to Collusive Agreements in Oligopoly Games.

In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of firms are shown to yield a wide range of different results.Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Externalities, Endogenous Coalition Formation.

Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

A conjectural cooperative equilibrium for strategic form games

This paper presents a new cooperative equilibrium for strategic form games, denoted Conjectural Cooperative Equilibrium (CCE). This concept is based on the expectation that joint deviations from any strategy profile are followed by an optimal and noncooperative reaction of non deviators. We show that CCE exist for all symmetric supermodular games. Furthermore, we discuss the existence of a CCE in specific submodular games employed in the literature on environmental agreements.Strong Nash Equilibrium, Cooperative Games, Public Goods

Advances in Negotiation Theory: Bargaining, Coalitions and Fairness

Bargaining is ubiquitous in real-life. It is a major dimension of political and business activities. It appears at the international level, when governments negotiate on matters ranging from economic issues (such as the removal of trade barriers), to global security (such as fighting against terrorism) to environmental and related issues (e.g. climate change control). What factors determine the outcome of negotiations such as those mentioned above? What strategies can help reach an agreement? How should the parties involved divide the gains from cooperation? With whom will one make alliances? This paper addresses these questions by focusing on a non-cooperative approach to negotiations, which is particularly relevant for the study of international negotiations. By reviewing noncooperative bargaining theory, non-cooperative coalition theory, and the theory of fair division, this paper will try to identify the connection among these different facets of the same problem in an attempt to facilitate the progress towards a unified framework.Negotiation theory, Bragaining, Coalitions, Fairness, Agreements

Advances in negotiation theory : bargaining, coalitions, and fairness

Bargaining is ubiquitous in real life. It is a major dimension of political and business activities. It appears at the international level, when governments negotiate on matters ranging from economic issues (such as the removal of trade barriers), to global security (such as fighting against terrorism) to environmental and related issues (such as climate change control). What factors determinethe outcomes of such negotiations? What strategies can help reach an agreement? How should the parties involved divide the gains from cooperation? With whom will one make alliances? The authors address these questions by focusing on a noncooperative approach to negotiations, which is particularly relevant for the study of international negotiations. By reviewing noncooperative bargaining theory, noncooperative coalition theory, and the theory of fair division, they try to identify the connections among these different facets of the same problem in an attempt to facilitate progress toward a unified framework.Economic Theory&Research,Social Protections&Assistance,Environmental Economics&Policies,Scientific Research&Science Parks,Science Education

Spectrum Leasing as an Incentive towards Uplink Macrocell and Femtocell Cooperation

The concept of femtocell access points underlaying existing communication infrastructure has recently emerged as a key technology that can significantly improve the coverage and performance of next-generation wireless networks. In this paper, we propose a framework for macrocell-femtocell cooperation under a closed access policy, in which a femtocell user may act as a relay for macrocell users. In return, each cooperative macrocell user grants the femtocell user a fraction of its superframe. We formulate a coalitional game with macrocell and femtocell users being the players, which can take individual and distributed decisions on whether to cooperate or not, while maximizing a utility function that captures the cooperative gains, in terms of throughput and delay.We show that the network can selforganize into a partition composed of disjoint coalitions which constitutes the recursive core of the game representing a key solution concept for coalition formation games in partition form. Simulation results show that the proposed coalition formation algorithm yields significant gains in terms of average rate per macrocell user, reaching up to 239%, relative to the non-cooperative case. Moreover, the proposed approach shows an improvement in terms of femtocell users' rate of up to 21% when compared to the traditional closed access policy.Comment: 29 pages, 11 figures, accepted at the IEEE JSAC on Femtocell Network