L favor with si . We further set a group Gi Gi
L favor with si . We further set a group Gi Gi fsi g including him herself. People today feel extra intimacy when they share what they like and what they don’t with the other group members. Which is, in our setup, if they likedislike the same individuals collectively, they feel that their group is a lot more integrated. This observation suggests that congruity Ci that the individual si experiences within the group Gi might be defined as an overall similarity among si plus the members of Gi . We set 8 X DDvi {vj DD, di DGi D sj [Gi : if DGi D if DGi Dan average distance between the feeling vector of si and those of the group members, where DGi D is the number of the individuals in Gi . Then the congruity of Gi is defined as Ci di . Note that, if pffiffiffi we use a 2, the range of Ci isfor some constant parameter a. Note that the feeling vectors v ,v2 , ,vn completely characterizes the current configuration and determines the group distribution, G ,G2 , ,Gn , and sense of belonging S ,S2 , ,Sn . Our basic assumption on group formation is that each individual keeps adjusting emotional attitudes toward others to maximize hisher sense of belonging. To trace dynamics of group formation, we use the best response rule: individuals, when they get a revision chance, adopt their best possible attitude toward others (best response) to the current configuration. This implies that an individual si updates the feeling vector vi to, say vi0, so that the virtual configuration v ,v2 , ,vi0, , vn leads to maximization of Si . For practical consideration, we assume that one changes his her attitude toward only one person at a time. That is, for each vi (vi, ,vi, , ,vi,n ), one picks just one component and switch its value from a to {a (or the other way around). If there are more than two possible choices for maximum, one of them is arbitrarily selected. The dynamical behaviour in evolutionary games generally depends on the choice of the update rules as well. In this work, we apply the synchronous update rule: in discrete time steps, the whole individuals s ,s2 , ,sn adjust their feeling vectors v ,v2 , ,vn simultaneously according to the best response rule mentioned above. JI-101 web However, it turned out that basic properties of the system are not influenced by update rules. The simulation results that follow in the next sections are qualitatively same for the sequentialrandom update rules.Results and Exclusion of an Accidental OutcastIn this section, we show that individual efforts to increase their sense of belonging lead to formation of groups, and moreover, toPLOS ONE plosone.orgA Simple Model of Ostracism Formationfrequent occurrence of ostracism. People’s preference to large and homogeneous groups is well explained from the form of the payoff in . In Figure 2, one can see a typical group formation of 30 people with the payoff functions and the update rule described in the previous section. The graphs in the upper figure are the evolving group sizes DGi D,i ,2, ,30 along this discrete time steps upto t ,2, ,40. In the initial configuration at t 0, we set the initial ratio of friendliness as low as 40 which implies that the probability of mutual friendliness between two arbitrary persons is 0:6: This explains that the most group sizes are around 5 at t 0. However, initiated from an arbitrary configuration, people PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/21425987 start to gather according to the evolutionary rule described in Section 2 and soon melt into a large group before t 30. The lower three figures show snapsho.
