An Algorithm for Generating Nash Stable Coalition Structures in Hedonic Games

2010 ◽  
pp. 25-39
Author(s):  
Helena Keinänen
Keyword(s):  
Coalition Structures ◽  
Stable Coalition ◽  
Hedonic Games

scholarly journals Testing stability properties in graphical hedonic games

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Hendrik Fichtenberger ◽  
Anja Rey
Keyword(s):  
Time Complexity ◽  
Coalition Structure ◽  
Property Testing ◽  
Core Stability ◽  
Bounded Degree ◽  
Coalition Structures ◽  
Input Size ◽  
Stable Coalition ◽  
Hedonic Games ◽  
The Stability

AbstractIn hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an $$\epsilon$$ ϵ -fraction of the input (e.g., the game’s preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, (contractual) individual stability, and core stability. While there is always a Nash-stable coalition structure (which also implies individually stable coalitions), we show that the existence of a perfect coalition structure is not tautological but can be tested. All our testers have one-sided error and time complexity that is independent of the input size.

scholarly journals Forming Probably Stable Communities with Limited Interactions

2019 ◽  
Vol 33 ◽  
pp. 2053-2060
Author(s):  
Ayumi Igarashi ◽  
Jakub Sliwinski ◽  
Yair Zick
Keyword(s):  
Interaction Network ◽  
Graph Structure ◽  
Interaction Graph ◽  
Community Needs ◽  
Underlying Graph ◽  
Coalition Structures ◽  
Stable Coalition ◽  
Hedonic Games ◽  
Connected Subgraphs ◽  
Stable Community

A community needs to be partitioned into disjoint groups; each community member has an underlying preference over the groups that they would want to be a member of. We are interested in finding a stable community structure: one where no subset of members S wants to deviate from the current structure. We model this setting as a hedonic game, where players are connected by an underlying interaction network, and can only consider joining groups that are connected subgraphs of the underlying graph. We analyze the relation between network structure, and one’s capability to infer statistically stable (also known as PAC stable) player partitions from data. We show that when the interaction network is a forest, one can efficiently infer PAC stable coalition structures. Furthermore, when the underlying interaction graph is not a forest, efficient PAC stabilizability is no longer achievable. Thus, our results completely characterize when one can leverage the underlying graph structure in order to compute PAC stable outcomes for hedonic games. Finally, given an unknown underlying interaction network, we show that it is NP-hard to decide whether there exists a forest consistent with data samples from the network.

scholarly journals Sequentially Stable Coalition Structures

2007 ◽  
Author(s):  
Yukihiko Funaki ◽  
Takehiko Yamato
Keyword(s):  
Coalition Structures ◽  
Stable Coalition

An algorithm for computing the stable coalition structures in tree-graph communication games

Top ◽  
1999 ◽  
Vol 7 (1) ◽  
pp. 71-80
Author(s):  
Fritz H. Grafe ◽  
Elena Inarra ◽  
Ana Mauleon
Keyword(s):  
Tree Graph ◽  
Coalition Structures ◽  
Communication Games ◽  
Stable Coalition

Potential functions for finding stable coalition structures

2019 ◽  
Vol 47 (6) ◽  
pp. 478-482
Author(s):  
Vasily V. Gusev ◽  
Vladimir V. Mazalov
Keyword(s):  
Potential Functions ◽  
Coalition Structures ◽  
Stable Coalition

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.

A Dynamic Game Approach for Analyzing the Coalitional Stability of Cascaded Hydropower Stations

2012 ◽  
Vol 562-564 ◽  
pp. 1544-1548
Author(s):  
Heng Li Song ◽  
Chao Yuan Yue
Keyword(s):  
Electricity Markets ◽  
Dynamic Game ◽  
Social Benefit ◽  
Western Region ◽  
Coalition Structures ◽  
The Social ◽  
Stable Coalition ◽  
Coalitional Stability ◽  
Dynamic Cooperation ◽  
Hydropower Stations

A game model is proposed to discuss the possible coalition structures of hydropower stations. The stable coalition structures in different contexts of electricity markets are derived on basic of numerical simulation using the raw data of three hydropower stations on the middle and lower reaches of some river in China's south-western region as a case. The coalitional stability is analyzed by a dynamic cooperation game approach using the conception of LCS and EPCS. The total purchase power fees of the grid in three coalition structures are calculated and compared to analyze the effects of coalition structures on the social benefit.

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