Stability and Segregation in Group Formation

Abstract

This paper presents a model of group formation based on the assumption that individuals prefer to associate with people similar to them. It is shown that, in general, if the number of groups that can be formed is bounded, then a stable Ž partition of the society into groups may not exist. A partition is defined as stable if . none of the individuals would prefer be in a different group than the one he is in. However, if individuals' characteristics are one-dimensional, then a stable partition always exists. We give sufficient conditions for stable partitions to be segregating Žin the sense that, for example, low-characteristic individuals are in one group and . high-characteristic ones are in another and Pareto efficient. In addition, we propose a dynamic model of individual myopic behavior describing the evolution of group formation to an eventual stable, segregating, and Pareto efficient partition. Journal of Economic Literature

Core in a simple coalition formation game

“…Their result dramatically contrasts the core in large games with the core in our finite games. Milchtaich & Winter [1997] introduce a model where (i) the number of coalitions is fixed, (ii) each agent is endowed with a number, and (iii) each agent prefers to be in a group which is most similar to herself on average. They show that a Nash stable partition exists that is segregating and Pareto efficient.…”

Strategic behaviour in Schelling dynamics: Theory and experimental evidence

“…This configuration is represented as a connected ring in Figure 1. Furthermore, let's suppose that each individual in configuration (1) accepts up to 11 This coincides with our definition of a myopic player.…”

“…This striking result has generated a vast amount of literature from a wide range of scientific trends. Miltaich and Winter (2002), assuming that individual's characteristics are unidimensional, find a stable partition that not only is stable but also segregating. Likewise, Karni and Schneidler (1990) examine the conditions for segregation and group formation in an overlapping generations model.…”

“…That is, when their turn to move comes, individuals move if their neighbourhood demands are not met, 11 and the typical outcome is a highly segregated society. The dynamics in Schelling's model can be defined as an iterative and sequential process of agents choosing myopic responses, where the only restriction to the mobility of agents is to go to the nearest place.…”

Nation Formation and Genetic Diversity

“…Thus, our nation formation game is a hedonic game. 6 Also, the contribution by Milchtaich and Winter (2002), where players compare groups on the basis of the distance between their own characteristics and the average characteristics of the group, share some common features with our work.…”