Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities

Abstract

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, 2011, for roomate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).

Axiomatic Foundations of a Unifying Core

“…Maskin monotonicity (Maskin, 1999) is one of the key principle in implementation theory but is also desirable in and of itself (see, for example, Kojima and Manea, 2010;Karakaya and Klaus, 2017). Roughly speaking, this axiom, called here Maskin invariance, 3 requires that if a state is chosen in an e-form game, then it is also chosen in an e-form game in which the state has (weakly) improved in the preference rankings of all players.…”

Koalisyon Oluşumu Oyunları: İçsel Kararlılık

“…Bir koalisyon yapısında, eğer hiçbir birey içinde yer aldığı koalisyonu terk edip kendi başına kaldığında ya da var olan başka bir koalisyona katıldığında daha mutlu olamıyor ise, bu koalisyon yapısına Nash kararlı denir (Bogomolnaia ve Jackson, 2002). En genel tanım kümesi 2 düşünüldüğünde çekirdek kararlı veya 1 Literatürde yer alan bazı kararlılık kavramlarının sınıflandırılması Sung ve Dimitrov (2007a) (Karakaya, 2011), (Karakaya ve Klaus, 2017), (Gallo ve Inarra, 2018) ve (Özbilen, 2019) incelenebilir. Tüm hedonik oyunlar kümesinde ya da bazı özel hedonik oyunlar kümelerinde kararlı koalisyon yapılarının bulunması veya verilen bir koalisyon yapısının kararlı olup olmadığının gösterilmesi ile alakalı hesaplama karmaşıklığı çalışmaları için (Ballester, 2004), (Sung ve Dimitrov, 2007b), (Sung ve Dimitrov, 2010), (Cechlarova ve Hajdukova, 2002), (Cechlarova ve Hajdukova, 2004a), ve (Cechlarova ve Hajdukova, 2004b) incelenebilir.…”

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

“…Another analytical approach used in the study of hedonic games is to restrict the form of the game to ensure core membership; this approach has been applied by some researchers (Alcalde & Romero-Medina, 2006;Apt & Witzel, 2009;Dimitrov, Borm, Hendrickx, & Sung, 2006;Hasan, Gorce, & Altman, 2020;Pápai, 2004). Others have created interesting variations of hedonic games to solve (Karakaya & Klaus, 2017). We are interested in knowing the general properties of hedonic games; that is, given a hedonic game, how frequently would expect the game not to be core stable?…”