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.

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 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 Stable and Envy-free Partitions in Hedonic Games

2019 ◽  
Author(s):  
Nathanaël Barrot ◽  
Makoto Yokoo
Keyword(s):  
Coalition Formation ◽  
Grand Coalition ◽  
Core Stability ◽  
Pareto Optimal ◽  
Hedonic Games ◽  
Np Complete ◽  
Stability Notions

In this paper, we study coalition formation in hedonic games through the fairness criterion of envy-freeness. Since the grand coalition is always envy-free, we focus on the conjunction of envy-freeness with stability notions. We first show that, in symmetric and additively separable hedonic games, an individually stable and justified envy-free partition may not exist and deciding its existence is NP-complete. Then, we prove that the top responsiveness property guarantees the existence of a Pareto optimal, individually stable, and envy-free partition, but it is not sufficient for the conjunction of core stability and envy-freeness. Finally, under bottom responsiveness, we show that deciding the existence of an individually stable and envy-free partition is NP-complete, but a Pareto optimal and justified envy-free partition always exists.

scholarly journals Relaxed Core Stability in Fractional Hedonic Games

2021 ◽  
Author(s):  
Angelo Fanelli ◽  
Gianpiero Monaco ◽  
Luca Moscardelli
Keyword(s):  
Coalition Formation ◽  
Core Stability ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
The Core ◽  
Utility Gain ◽  
Tiny Amount ◽  
Multi Agent ◽  
Hedonic Games ◽  
Stable Solutions

The core is a well-known and fundamental notion of stability in games intended to model coalition formation such as hedonic games. The fact that the number of deviating agents (that have to coordinate themselves) can be arbitrarily high, and the fact that agents may benefit only by a tiny amount from their deviation (while they could incur in a cost for deviating), suggest that the core is not able to suitably model many practical scenarios in large and highly distributed multi-agent systems. For this reason, we consider relaxed core stable outcomes where the notion of permissible deviations is modified along two orthogonal directions: the former takes into account the size of the deviating coalition, and the latter the amount of utility gain for each member of the deviating coalition. These changes result in two different notions of stability, namely, the q-size core and k-improvement core. We investigate these concepts of stability in fractional hedonic games, that is a well-known subclass of hedonic games for which core stable outcomes are not guaranteed to exist and it is computationally hard to decide nonemptiness of the core. Interestingly, the considered relaxed notions of core also possess the appealing property of recovering, in some notable cases, the convergence, the existence and the possibility of computing stable solutions in polynomial time.

Core Stability, Part 2: The Core-Extremity Link

2012 ◽  
Vol 17 (2) ◽  
pp. 10-15 ◽  
Author(s):  
Marisa A. Colston
Keyword(s):  
Core Stability ◽  
The Core

scholarly journals Influence of foam rolling on the functional limitations of the musculoskeletal system in healthy women

2017 ◽  
Vol 9 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Dariusz Boguszewski ◽  
Magdalena Falkowska ◽  
Jakub Grzegorz Adamczyk ◽  
Dariusz Białoszewski
Keyword(s):  
Muscle Strength ◽  
Musculoskeletal System ◽  
Lower Limb ◽  
Functional Limitations ◽  
Core Stability ◽  
Stability Test ◽  
Physical Effort ◽  
Foam Rolling ◽  
The Core ◽  
Group 1

Summary Study aim: To determine the effect of foam rolling on the functional limitations of the musculoskeletal system.Material and methods: The study encompassed 37 healthy and physically active women divided into two groups. Group 1 comprised women who performed self-massage with a foam roller after physical effort twice a week, for two months. Group 2 (control) comprised women who did not undergo any exercises or treatment after physical effort. The study used the following research tools: the Functional Movement Screen (FMS) test, the Core Muscle Strength and Stability Test (CMS&ST), and the Sit and Reach Test.Results: The study revealed that foam rolling minimized functional limitations (as measured with the FMS test). The differences between the first and second measurement in Group 1 were statistically significant (p=0.014). In the control group, the results of both measurements were similar. In the CMS&ST, the maximal result of three minutes was not achieved. Moreover, no improvement of results was observed. In the Sit and Reach Test, a statistically significant improvement in the flexibility of the posterior muscles of the thigh was noted in Group 1 (right lower limb p=0.009, left lower limb p = 0.007).Conclusions: 1. Foam rolling may minimize the functional limitations of the musculoskeletal system. It is recommended to incorporate self-myofascial release techniques after physical effort into training. 2. Using foam rolling helped maintain the results obtained in the Core Muscle Strength and Stability Test. Therefore, foam rolling may help maintain the achieved core stability.

scholarly journals MPF Problem over Modified Medial Semigroup Is NP-Complete

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 571 ◽  
Author(s):  
Eligijus Sakalauskas ◽  
Aleksejus Mihalkovich
Keyword(s):  
Power Function ◽  
Polynomial Time ◽  
Cryptographic Protocols ◽  
Binary Field ◽  
Dual Interpretation ◽  
Np Complete ◽  
Matrix Power ◽  
Necessary Constraints ◽  
One Way Function ◽  
Polynomial Time Reduction

This paper is a continuation of our previous publication of enhanced matrix power function (MPF) as a conjectured one-way function. We are considering a problem introduced in our previous paper and prove that tis problem is NP-Complete. The proof is based on the dual interpretation of well known multivariate quadratic (MQ) problem defined over the binary field as a system of MQ equations, and as a general satisfiability (GSAT) problem. Due to this interpretation the necessary constraints to MPF function for cryptographic protocols construction can be added to initial GSAT problem. Then it is proved that obtained GSAT problem is NP-Complete using Schaefer dichotomy theorem. Referencing to this result, GSAT problem by polynomial-time reduction is reduced to the sub-problem of enhanced MPF, hence the latter is NP-Complete as well.

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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