Nash Stability in Social Distance Games

In this paper we focus on Social Distance Games (SDGs), Coalition formation is a pervasive aspect of social life and an important subclass of HGs introduced in (Brânzei and it has been studied extensively in algorithmic game theory Larson 2011) where agent utilities are based on the concept using the natural model of Hedonic Games (HGs), introduced of social distance (i.e., the number of hops required to reach in (Dreze and Greenberg 1980) and further explored one node from another), which has become famous since in (Aziz, Brandt, and Harrenstein 2011; Aziz, Brandt, and Milgram's study on six degrees of separation. In SDGs the Seedig 2013; Banerjee, Konishi, and Sönmez 2001; Bogomolnaia utility of an agent is given by the average inverse distance and Jackson 2002; Elkind and Wooldridge 2009; from all the other nodes in her coalition, that is by her harmonic Elkind, Fanelli, and Flammini 2016; Gairing and Savani centrality (Boldi and Vigna 2014) divided by the size 2010). A HG consists of a set of selfish agents (humans, of the coalition. The basic idea is that the agents prefer to robots, software agents, etc.) having preferences over coalitions maintain ties with other agents who are close to them. The that might include them, regardless of which other utility formulation is a variant of the closeness centrality and coalitions may or may not be present. The outcome is a partition reflects the principle of homophily, that similarity breeds of the agent set into disjoint coalitions (or clusters), connection and people tend to form communities with similar referred to as a clustering or coalition structure.