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 Core Stability in Hedonic Games among Friends and Enemies: Impact of Neutrals

2017 ◽  
Author(s):  
Kazunori Ohta ◽  
Nathanaël Barrot ◽  
Anisse Ismaili ◽  
Yuko Sakurai ◽  
Makoto Yokoo
Keyword(s):  
Polynomial Time ◽  
Coalition Structure ◽  
Core Stability ◽  
The Core ◽  
Stable Coalition ◽  
Hedonic Games ◽  
Np Complete ◽  
Strict Core

We investigate hedonic games under enemies aversion and friends appreciation, where every agent considers other agents as either a friend or an enemy. We extend these simple preferences by allowing each agent to also consider other agents to be neutral. Neutrals have no impact on her preference, as in a graphical hedonic game.Surprisingly, we discover that neutral agents do not simplify matters, but cause complexity. We prove that the core can be empty under enemies aversion and the strict core can be empty under friends appreciation. Furthermore, we show that under both preferences, deciding whether the strict core is non-empty, is NP^NP-complete. This complexity extends to the core under enemies aversion. We also show that under friends appreciation, we can always find a core stable coalition structure in polynomial time.

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.

scholarly journals Unknown Agents in Friends Oriented Hedonic Games: Stability and Complexity

2019 ◽  
Vol 33 ◽  
pp. 1756-1763 ◽  
Author(s):  
Nathanaël Barrot ◽  
Kazunori Ota ◽  
Yuko Sakurai ◽  
Makoto Yokoo
Keyword(s):  
Negative Impact ◽  
Coalition Structure ◽  
The Core ◽  
Stable Coalition ◽  
Hedonic Games ◽  
Np Complete

We study hedonic games under friends appreciation, where each agent considers other agents friends, enemies, or unknown agents. Although existing work assumed that unknown agents have no impact on an agent’s preference, it may be that her preference depends on the number of unknown agents in her coalition. We extend the existing preference, friends appreciation, by proposing two alternative attitudes toward unknown agents, extraversion and introversion, depending on whether unknown agents have a slightly positive or negative impact on preference. When each agent prefers coalitions with more unknown agents, we show that both core stable outcomes and individually stable outcomes may not exist. We also prove that deciding the existence of the core and the existence of an individual stable coalition structure are respectively NPNP-complete and NP-complete.

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

scholarly journals Generating Empirical Core Size Distributions of Hedonic Games Using a Monte Carlo Method

2021 ◽  
pp. 2250001
Author(s):  
Andrew J. Collins ◽  
Sheida Etemadidavan ◽  
Wael Khallouli
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Numerical Approach ◽  
Core Stability ◽  
Size Distributions ◽  
Core Size ◽  
Empirical Distributions ◽  
Research Findings ◽  
Hedonic Games ◽  
Partition Size

Hedonic games have gained popularity over the last two decades, leading to several research articles that have used analytical methods to understand their properties better. In this paper, a Monte Carlo method, a numerical approach, is used instead. Our method includes a technique for representing, and generating, random hedonic games. We were able to create and solve, using core stability, millions of hedonic games with up to 16 players. Empirical distributions of the hedonic games’ core sizes were generated, using our results, and analyzed for games of up to 13 players. Results from games of 14–16 players were used to validate our research findings. Our results indicate that core partition size might follow the gamma distribution for games with a large number of players.

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