A Simple Model of Coevolution for Macroscopic and Microscopic Levels

In Thomas Schelling's famous segregation model, it is shown that the link between the individual characteristics of agents (micro) and the global states of the system (macro) is not trivial. By the use of statistical physics tools [1] it was, nevertheless possible, to establish an analytical link between these two levels, characteristics of agents (utility function) and global structures of segregation. This work aims to build a similar conceptual model, but includes an important sociological ingredient: the evolution of individual characteristics. Economic models have often been subject to criticism (by sociologists, mainly) about their arbitrary and static set of individual characteristics. In our approach we thus blend in the the standard segregation model a simple co-evolution mechanism of micro and macro levels in order to encompass, at least to some extent, the aforementioned limitation. More specifically, we add a feedback mechanism linking the agents' interactions and their individual characteristics. The most dramatic departure from the standard model regards the movement rule as we endow the agents with the possibility of wisely deciding their relocation target and, moreover, this choice is informed both by their own personal preferences and by their social ties' ones. In practice, instead of picking a different random empty cell on the lattice, unhappy agents move to the location which better suits their preferences, albeit with some noise. An adaptive decision mechanism is implemented in form of a per-agent “palatability” matrix , the size of the whole lattice, which is initialized with average values. As soon as agents appear in the model, they evaluate their location (standard Moore neighborhood) and establish links with their neighbors (proportional to their tolerance: 0 = same type only, 1 = equally split between types) on an undirected and unweighted graph. During each iteration of the model, each agent evaluates the option of either staying or leaving, given her tolerance threshold. In the latter case, the relocation target is decided mixing both the agent's personal preferences and its acquaintances': for instance, one possible strategy is to built a final decisional matrix from the personal matrix , and the connected agents' matrices, , linearly weighted by a given “stubbornness” parameter , For the sake of simplicity, connected agents are averaged with equal weight. The absolute best tile is taken as the destination. With this approach, we thus aim to study the co-evolution of preferences and global states in order to identify possible stationary states (at both levels). References [1] Grauwin, Sebastian, et al., “Competition between collective and individual dynamics.” Proceedings of the National Academy of Sciences, 2009, vol. 106, n. 49, pp. 20622-20626. This work was performed within the framework of the LABEX MILYON (ANR-10- LABX-0070) of Universite de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).