Cooperative congestion games: existence of a Nash-stable coalition structure

2022 ◽  
Author(s):  
Vasily V. Gusev
Keyword(s):  
Coalition Structure ◽  
Congestion Games ◽  
Stable Coalition

Stable Coalition Structure of Patent Technologies

2019 ◽  
Vol 27 (2) ◽  
pp. 1-42
Author(s):  
Hyukseung Shin ◽  
Insuk Cheong
Keyword(s):  
Coalition Structure ◽  
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.

Stochastic Approach for Determining Stable Coalition Structure

2015 ◽  
Vol 17 (04) ◽  
pp. 1550009 ◽  
Author(s):  
Elena Parilina ◽  
Artem Sedakov
Keyword(s):  
Markov Chain ◽  
Nash Equilibrium ◽  
Special Form ◽  
Stochastic Game ◽  
Coalition Structure ◽  
Stochastic Approach ◽  
Tu Games ◽  
Absorbing State ◽  
Stable Coalition ◽  
Definition Of

In this paper, we study TU-games with coalition structure and propose an approach for determining a stable coalition structure solving a stochastic game of a special form. Using a Nash equilibrium in this game, we draw an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider a case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of the stable coalition structure to this case.

scholarly journals COALITION FORMATION IN GAMES WITHOUT SYNERGIES

2006 ◽  
Vol 08 (01) ◽  
pp. 111-126 ◽  
Author(s):  
SERGIO CURRARINI ◽  
MARCO A. MARINI
Keyword(s):  
Coalition Formation ◽  
Sufficient Conditions ◽  
Coalition Structure ◽  
Strategic Complementarity ◽  
Form Game ◽  
Stable Coalition ◽  
Unanimity Game

This paper establishes sufficient conditions for the existence of a stable coalition structure in the "coalition unanimity" game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2003). Our conditions are defined on the strategic form game used to derive the payoffs of the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions.

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.

THE AUMANN-DRÈZE VALUE, THE WIESE VALUE, AND STABILITY: A NOTE

2010 ◽  
Vol 12 (02) ◽  
pp. 189-195 ◽  
Author(s):  
ANDREAS TUTIC
Keyword(s):  
Coalition Structure ◽  
Tu Game ◽  
Stable Coalition

In this note we present an example of a TU game where both the value presented by Aumann and Drèze (1974) and the value introduced by Wiese (2007) do not exhibit a stable coalition structure.

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.

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