scholarly journals Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1965
Author(s):  
Jun Su ◽  
Yuan Liang ◽  
Guangmin Wang ◽  
Genjiu Xu
Keyword(s):  
Potential Function ◽  
Cooperative Games ◽  
Coalition Structure ◽  
Balanced Contributions ◽  
Bidding Mechanism

In this paper, we provide cooperative and non-cooperative interpretations of the Shapley–Solidarity value for cooperative games with coalition structure. Firstly, we present two new characterizations of this value based on intracoalitional quasi-balanced contributions property. Secondly, we study a potential function of the Shapley–Solidarity value. Finally, we propose a new bidding mechanism for the Solidarity value and then apply the result to the Shapley–Solidarity value.

The weighted Shapley-egalitarian value for cooperative games with a coalition structure

Top ◽  
2019 ◽  
Vol 28 (1) ◽  
pp. 193-212 ◽  
Author(s):  
Xun-Feng Hu
Keyword(s):  
Cooperative Games ◽  
Coalition Structure ◽  
Egalitarian Value

Applying Cooperative Games with Coalition Structure for Data Clustering

2019 ◽  
Vol 80 (8) ◽  
pp. 1541-1551
Author(s):  
V. M. Bure ◽  
K. Yu. Staroverova
Keyword(s):  
Data Clustering ◽  
Cooperative Games ◽  
Coalition Structure

scholarly journals Cooperative Games with Overlapping Coalitions

2010 ◽  
Vol 39 ◽  
pp. 179-216 ◽  
Author(s):  
G. Chalkiadakis ◽  
E. Elkind ◽  
E. Markakis ◽  
M. Polukarov ◽  
N. R. Jennings
Keyword(s):  
Coalition Formation ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Coalition Structure ◽  
Coalitional Games ◽  
The Core ◽  
Coalition Structures ◽  
Coalition Formation Process ◽  
The Social ◽  
Overlapping Coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

Cooperative games on convex geometries with a coalition structure

2012 ◽  
Vol 25 (5) ◽  
pp. 909-925 ◽  
Author(s):  
Fanyong Meng ◽  
Qiang Zhang
Keyword(s):  
Cooperative Games ◽  
Coalition Structure ◽  
Convex Geometries

scholarly journals An axiomatic and non-cooperative approach to the multi-step Shapley value

2021 ◽  
Author(s):  
Xianghui Li ◽  
Yang Li
Keyword(s):  
Nash Equilibrium ◽  
Shapley Value ◽  
Cooperative Games ◽  
Cooperative Approach ◽  
Subgame Perfect Nash Equilibrium ◽  
Bidding Mechanism

Inspired by the two-step Shapley value, in this paper we introduce and axiomatize the multi-step Shapley value for cooperative games with levels structures. Moreover, we design a multi-step bidding mechanism, which implements the value strategically in subgame perfect Nash equilibrium for superadditve games.

Stable Cooperation in a Game with a Major Player

2016 ◽  
Vol 18 (02) ◽  
pp. 1640005 ◽  
Author(s):  
Elena Parilina ◽  
Artem Sedakov
Keyword(s):  
Nash Equilibrium ◽  
Cooperative Games ◽  
Coalition Structure ◽  
Star Graph ◽  
Communication Structure ◽  
Myerson Value ◽  
Coalition Structures ◽  
Restricted Cooperation ◽  
Major Player ◽  
Analytical Expressions

The theory of cooperative games with restricted cooperation has been rapidly developing over the last decades. In our study, we present a special game with restricted cooperation — a game with a major player — a modified version of the landlord game presented in Moulin [1988]. Cooperation of players is supposed to be restricted by a communication structure (a star-graph) as well as a coalition structure. We adopt two well-known cooperative allocations — the Myerson value and the ES-value — to the case when there exist restrictions on the cooperation of players and provide their analytical expressions. Additionally, we examine stability of coalition structures using the concept of the Nash equilibrium and formulate conditions guaranteeing such stability for a given coalition structure.

Coalition structure generation in cooperative games with compact representations

2018 ◽  
Vol 32 (4) ◽  
pp. 503-533 ◽  
Author(s):  
Suguru Ueda ◽  
Atsushi Iwasaki ◽  
Vincent Conitzer ◽  
Naoki Ohta ◽  
Yuko Sakurai ◽  
...  
Keyword(s):  
Cooperative Games ◽  
Coalition Structure ◽  
Structure Generation ◽  
Compact Representations ◽  
Coalition Structure Generation

A proportional value for cooperative games with a coalition structure

2014 ◽  
Vol 78 (2) ◽  
pp. 273-287 ◽  
Author(s):  
Frank Huettner
Keyword(s):  
Cooperative Games ◽  
Coalition Structure ◽  
Proportional Value

Balanced Contributions Axiom in the Solution of Cooperative Games

1997 ◽  
Vol 20 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Francisco Sánchez S.
Keyword(s):  
Cooperative Games ◽  
Balanced Contributions

The Feasible Coalitional Structures in the Weighted Cooperative Games

2015 ◽  
Vol 713-715 ◽  
pp. 1963-1966
Author(s):  
Shao Bai Chen ◽  
Zhao Di Hu ◽  
Man Zhang
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Coalition Structure ◽  
Coalitional Structure ◽  
Coalition Structures ◽  
Feasible Coalition

In cooperative games, the formation of coalitional structure and their allocation are important problems. This paper firstly for participants with different position or itself by the relative inseparable coalition composition, put forward weighted cooperative game. The formations of feasible coalition structure are presented. On the basis of the revenues in all feasible coalition structures for every participant, their allocation indexes are determined and based on the allocation indexes, the revenue of the biggest coalitional structure be assigned to each participant. This method's reasonability represents that the participants' allocation indexes are from the competition among individuals and maximizing the overall revenue reflects all participants' cooperation.

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