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.

The Core of Aggregative Cooperative Games with Externalities

2016 ◽  
Vol 16 (1) ◽  
pp. 389-410 ◽  
Author(s):  
Giorgos Stamatopoulos
Keyword(s):  
Normal Form ◽  
Characteristic Function ◽  
Coalition Formation ◽  
Cooperative Games ◽  
Grand Coalition ◽  
Normal Form Games ◽  
The Core ◽  
Aggregative Games ◽  
Games With Externalities

AbstractThis paper analyzes cooperative games with externalities generated by aggregative normal form games. We construct the characteristic function of a coalition S for various coalition formation rules and we examine the corresponding cores. We first show that the $$\gamma $$-core is non-empty provided each player’s payoff decreases in the sum of all players’ strategies. We generalize this result by showing that if S believes that the outside players form at least $$l(s) = n - s - (s - 1)$$ coalitions, then S has no incentive to deviate from the grand coalition and the corresponding core is non-empty (where n is the number of players in the game and s the number of members of S). We finally consider the class of linear aggregative games (Martimort and Stole 2010). In this case, if S believes that the outsiders form at least $$\widehat l(s) = {n \over s} - 1$$ coalitions [where $$\widehat l(s) \le l(s)$$] a core non-emptiness result holds again.

STABLE COALITION STRUCTURES UNDER RESTRICTED COALITIONAL CHANGES

2014 ◽  
Vol 16 (03) ◽  
pp. 1450006 ◽  
Author(s):  
YUKIHIKO FUNAKI ◽  
TAKEHIKO YAMATO
Keyword(s):  
Coalition Formation ◽  
Sufficient Conditions ◽  
Coalition Structure ◽  
Grand Coalition ◽  
Cournot Oligopoly ◽  
Common Pool Resource ◽  
Common Pool ◽  
Coalition Structures ◽  
Stable Coalition ◽  
Stability Concept

In this paper, we examine whether farsighted players form the efficient grand coalition structure in coalition formation games. We propose a stability concept for a coalition structure, called sequentially stability, when only bilateral mergers of two separate coalitions are feasible because of high negotiation costs. We provide an algorithm to check the sequential stability of the grand coalition structure as well as sufficient conditions for which the efficient grand coalition structure is sequentially stable. We also illustrate out results by means of common pool resource games and Cournot oligopoly games.

Cooperative games and multiagent systems

2013 ◽  
Vol 28 (4) ◽  
pp. 381-424 ◽  
Author(s):  
Stéphane Airiau
Keyword(s):  
Game Theory ◽  
Sensor Networks ◽  
Web Services ◽  
Multiagent Systems ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Coalitional Games ◽  
Electronic Marketplaces ◽  
Key Issues

AbstractForming coalitions is a generic means for cooperation: people, robots, web services, resources, firms; they can all improve their performance by joining forces. The use of coalitions has been successful in domains such as task allocations, sensor networks, and electronic marketplaces. Forming efficient coalitions requires the identification of matching synergies between different entities (finding complementary partners, or similar partners, or partners who add diversity). In addition, the different parties must negotiate a fair repartition of the worth created by the coalition. The first part of this paper is a tutorial on cooperative game theory (also called coalitional games). We then survey the different scenarios and the key issues addressed by the multiagent systems community.

scholarly journals Nonadditive integration and some solutions of cooperative games

2021 ◽  
Vol 13 (1) ◽  
pp. 5-27
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Support Function ◽  
Cooperative Game Theory ◽  
Measurable Space ◽  
Symmetric Power ◽  
Infinite Games ◽  
The Core ◽  
Universal Approach ◽  
Set Function

In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.

scholarly journals Manipulation of k-Coalitional Games on Social Networks

2021 ◽  
Author(s):  
Naftali Waxman ◽  
Sarit Kraus ◽  
Noam Hazon
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Social Welfare ◽  
Coalition Formation ◽  
The Other ◽  
Full Information ◽  
Limited Information ◽  
Coalitional Games ◽  
Other Hand ◽  
The Social

In many coalition formation games the utility of the agents depends on a social network. In such scenarios there might be a manipulative agent that would like to manipulate his connections in the social network in order to increase his utility. We study a model of coalition formation in which a central organizer, who needs to form k coalitions, obtains information about the social network from the agents. The central organizer has her own objective: she might want to maximize the utilitarian social welfare, maximize the egalitarian social welfare, or only guarantee that every agent will have at least one connection within her coalition. In this paper we study the susceptibility for manipulation of these objectives, given the abilities and information that the manipulator has. Specifically, we show that if the manipulator has very limited information, namely he is only familiar with his immediate neighbours in the network, then a manipulation is almost always impossible. Moreover, if the manipulator is only able to add connections to the social network, then a manipulation is still impossible for some objectives, even if the manipulator has full information on the structure of the network. On the other hand, if the manipulator is able to hide some of his connections, then all objectives are susceptible to manipulation, even if the manipulator has limited information, i.e., when he is familiar with his immediate neighbours and with their neighbours.

USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004 ◽  
Author(s):  
CAMELIA BEJAN ◽  
JUAN CAMILO GÓMEZ
Keyword(s):  
Nash Equilibrium ◽  
Coalition Formation ◽  
Solution Concept ◽  
Transferable Utility ◽  
Tu Game ◽  
Subgame Perfect Nash Equilibrium ◽  
The Core ◽  
Core Solution ◽  
Aspiration Core ◽  
Overlapping Coalitions

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

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.

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.

scholarly journals Loyalty in Cardinal Hedonic Games

2021 ◽  
Author(s):  
Martin Bullinger ◽  
Stefan Kober
Keyword(s):  
Coalition Formation ◽  
Pareto Optimal ◽  
Common Theme ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
The Core ◽  
Coalition Structures ◽  
Group Stability ◽  
Multi Agent ◽  
Hedonic Games

A common theme of decision making in multi-agent systems is to assign utilities to alternatives, which individuals seek to maximize. This rationale is questionable in coalition formation where agents are affected by other members of their coalition. Based on the assumption that agents are benevolent towards other agents they like to form coalitions with, we propose loyalty in hedonic games, a binary relation dependent on agents' utilities. Given a hedonic game, we define a loyal variant where agents' utilities are defined by taking the minimum of their utility and the utilities of agents towards which they are loyal. This process can be iterated to obtain various degrees of loyalty, terminating in a locally egalitarian variant of the original game. We investigate axioms of group stability and efficiency for different degrees of loyalty. Specifically, we consider the problem of finding coalition structures in the core and of computing best coalitions, obtaining both positive and intractability results. In particular, the limit game possesses Pareto optimal coalition structures in the core.

Ways and Voices in the Psychoanalysis of Links According to Enrique Pichon-Rivière

2016 ◽  
Vol 6 (2) ◽  
Author(s):  
Rosa Jaitin
Keyword(s):  
Couple Therapy ◽  
Clinical Observation ◽  
Clinical Work ◽  
The Core ◽  
The Social ◽  
The 1960S ◽  
Definition Of ◽  
Relationship Of ◽  
The Voice ◽  
Different Levels

This article covers several stages of the work of Pichon-Rivière. In the 1950s he introduced the hypothesis of "the link as a four way relationship" (of reciprocal love and hate) between the baby and the mother. Clinical work with psychosis and psychosomatic disorders prompted him to examine how mental illness arises; its areas of expression, the degree of symbolisation, and the different fields of clinical observation. From the 1960s onwards, his experience with groups and families led him to explore a second path leading to "the voices of the link"—the voice of the internal family sub-group, and the place of the social and cultural voice where the link develops. This brought him to the definition of the link as a "bi-corporal and tri-personal structure". The author brings together the different levels of the analysis of the link, using as a clinical example the process of a psychoanalytic couple therapy with second generation descendants of a genocide within the limits of the transferential and countertransferential field. Body language (the core of the transgenerational link) and the couple's absences and presence during sessions create a rhythm that gives rise to an illusion, ultimately transforming the intersubjective link between the partners in the couple and with the analyst.

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