The central core and the mid-central core as novel set-valued and point-valued solution concepts for transferable utility coalitional games

Coalitional games serve the purpose of modeling payoff distribution problems in scenarios where agents can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. In the classical Transferable Utility (TU) setting, coalition worths can be freely distributed amongst agents. However, in several application scenarios, this is not the case and the Non-Transferable Utility setting (NTU) must be considered, where additional application-oriented constraints are imposed on the possible worth distributions. In this paper, an approach to define NTU games is proposed which is based on describing allowed distributions via a set of mixed-integer linear constraints applied to an underlying TU game. It is shown that such games allow non-transferable conditions on worth distributions to be specified in a natural and succinct way. The properties and the relationships among the most prominent solution concepts for NTU games that hold when they are applied on (mixed-integer) constrained games are investigated. Finally, a thorough analysis is carried out to assess the impact of issuing constraints on the computational complexity of some of these solution concepts.

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Coalition formation and history dependence

Theoretical Economics ◽

10.3982/te2947 ◽

2020 ◽

Vol 15 (1) ◽

pp. 159-197 ◽

Cited By ~ 3

Author(s):

Bhaskar Dutta ◽

Hannu Vartiainen

Keyword(s):

Coalition Formation ◽

Stable Set ◽

Transferable Utility ◽

Stable Sets ◽

Solution Concepts ◽

History Dependence ◽

Von Neumann ◽

Finite Games ◽

A Chain ◽

Indirect Dominance

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann–Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional “moves” in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history‐independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta–Vohra analysis by allowing for history‐dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.

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Coalitional games with transferable utility

10.1017/9781108636049.019 ◽

2020 ◽

pp. 709-734

Keyword(s):

Transferable Utility ◽

Coalitional Games

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Solution Concepts for Coalitional Games in Constructing Networks

Multi-Objective Programming and Goal Programming ◽

10.1007/978-3-540-36510-5_37 ◽

2003 ◽

pp. 257-262

Author(s):

Masayo Tsurumi ◽

Tetsuzo Tanino ◽

Masahiro Inuiguchi

Keyword(s):

Coalitional Games ◽

Solution Concepts

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The Tractability of the Shapley Value over Bounded Treewidth Matching Games

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/145 ◽

2017 ◽

Cited By ~ 1

Author(s):

Gianluigi Greco ◽

Francesco Lupia ◽

Francesco Scarcello

Keyword(s):

Polynomial Time ◽

Shapley Value ◽

Open Problem ◽

Positive Answer ◽

Coalitional Games ◽

Solution Concepts ◽

Bounded Treewidth ◽

The Shapley Value ◽

Matching Games

Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them {solution concepts}. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whether or not this tractability result holds over classes of graphs properly including acyclic ones. The main contribution of the paper is to provide a positive answer to this question, by showing that the Shapley value is tractable for matching games defined over graphs having bounded treewidth. The proposed technique has been implemented and tested on classes of graphs having different sizes and treewidth at most three.

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Bargaining in n -person cooperative games with linearly distributed, transferable utility

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1995.0130 ◽

1995 ◽

Vol 451 (1942) ◽

pp. 349-365 ◽

Cited By ~ 1

Keyword(s):

Cooperative Games ◽

Binary Trees ◽

Transferable Utility ◽

Solution Concepts ◽

Coalition Structures ◽

Player Game ◽

The Subject ◽

Simply Connected

Coalitional aspects of bargaining are investigated. Binary trees describe coalition structures; at a vertex the payoffs are distributed linearly according to parameters for the two sets. The parameter for a player-set is assumed to be the sum of the parameters in that set. These values are the subject of bargaining. The criteria for the results of bargaining are formulated, thus determining a bargaining point(s) in the space R of the parameters. R can be divided into regions in which a particular tree is maximal. In completely essential 3-player games these regions are simply connected; the bargaining point is where these regions meet. The solutions for 4- and n -player games present immense problems. Our solutions are compared with other solution concepts. We show that in the 3-player game our solution is monotonic but not completely coalitionally monotonic.

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