Stable Cooperation in a Game with a Major Player

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.

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Cooperative Games with Overlapping Coalitions

Journal of Artificial Intelligence Research ◽

10.1613/jair.3075 ◽

2010 ◽

Vol 39 ◽

pp. 179-216 ◽

Cited By ~ 59

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 coalitionsor 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.

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The Myerson value for cooperative games on communication structure with fuzzy coalition

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-16080 ◽

2017 ◽

Vol 33 (1) ◽

pp. 27-39 ◽

Cited By ~ 4

Author(s):

Genjiu Xu ◽

Xianghui Li ◽

Hao Sun ◽

Jun Su

Keyword(s):

Cooperative Games ◽

Communication Structure ◽

Myerson Value

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The Feasible Coalitional Structures in the Weighted Cooperative Games

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.713-715.1963 ◽

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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The average tree solution for cooperative games with communication structure

Games and Economic Behavior ◽

10.1016/j.geb.2009.10.002 ◽

2010 ◽

Vol 68 (2) ◽

pp. 626-633 ◽

Cited By ~ 38

Author(s):

P.J.J. Herings ◽

G. van der Laan ◽

A.J.J. Talman ◽

Z. Yang

Keyword(s):

Cooperative Games ◽

Communication Structure

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Uncertain production environment and communication structure: the Bayesian Myerson value

SSRN Electronic Journal ◽

10.2139/ssrn.3935956 ◽

2021 ◽

Author(s):

Rodrigue Tido Takeng

Keyword(s):

Production Environment ◽

Communication Structure ◽

Myerson Value

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Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player

Risks ◽

10.3390/risks8040133 ◽

2020 ◽

Vol 8 (4) ◽

pp. 133

Author(s):

Olivier Féron ◽

Peter Tankov ◽

Laura Tinsi

Keyword(s):

Nash Equilibrium ◽

Electricity Markets ◽

Mean Field ◽

Optimal Strategies ◽

Price Formation ◽

Mean Field Games ◽

Optimal Trading ◽

Major Player ◽

Major Producer ◽

Small Producers

We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in a closed form in the asymptotic framework of mean field games with a major player.

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