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 Altruism in Coalition Formation Games

2020 ◽  
Author(s):  
Anna Maria Kerkmann ◽  
Jörg Rothe
Keyword(s):  
Coalition Formation ◽  
Computational Analysis ◽  
Altruistic Behavior ◽  
Major Disadvantage ◽  
Hedonic Games ◽  
Stability Notions

Nguyen et al. [2016] introduced altruistic hedonic games in which agents’ utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing the two models, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems.

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 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.

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.

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.

scholarly journals Simple Priorities and Core Stability in Hedonic Games

2004 ◽  
Author(s):  
Dinko Dimitrov ◽  
Peter E. M. Borm ◽  
Ruud Hendrickx ◽  
Shao Chin Sung
Keyword(s):  
Core Stability ◽  
Hedonic Games

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.

scholarly journals Subordinated Hedonic Games

Game Theory ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Juan Carlos Cesco
Keyword(s):  
Coalition Formation ◽  
Existence Result ◽  
Solution Concept ◽  
Stable Matching ◽  
Existence Problem ◽  
New Class ◽  
The Core ◽  
Reduced Game ◽  
Marriage Model ◽  
Hedonic Games

Hedonic games are simple models of coalition formation whose main solution concept is that of core partition. Several conditions guaranteeing the existence of core partitions have been proposed so far. In this paper, we explore hedonic games where a reduced family of coalitions determines the development of the game. We allow each coalition to select a subset of it so as to act as its set of representatives (a distribution). Then, we introduce the notion of subordination of a hedonic game to a given distribution. Subordination roughly states that any player chosen as a representative for a coalition has to be comfortable with this decision. With subordination we have a tool, within hedonic games, to compare how a “convenient” agreement reached by the sets of representatives of different groups of a society is “valued” by the rest of the society. In our approach, a “convenient” agreement is a core partition, so this paper is devoted to relate the core of a hedonic game with the core of a hedonic game played by the sets of representatives. Thus we have to tackle the existence problem of core partitions in a reduced game where the only coalitions that matter are those prescribed by the distribution as a set of representatives. We also study how a distribution determines the whole set of core partitions of a hedonic game. As an interesting example, we introduce the notion of hedonic partitioning game, which resembles partitioning games studied in the case where a utility, transferable or not, is present. The existence result obtained in this new class of games is later used to provide a nonconstructive proof of the existence of a stable matching in the marriage model.

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.

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