Schelling Segregation with Strategic Agents

Abstract

Schelling's segregation model is a landmark model in sociology. It shows the counterintuitive phenomenon that residential segregation between individuals of different groups can emerge even when all involved individuals are tolerant. Although the model is widely studied, no pure game-theoretic version where rational agents strategically choose their location exists. We close this gap by introducing and analyzing generalized game-theoretic models of Schelling segregation, where the agents can also have individual location preferences.For our models we investigate the convergence behavior and the efficiency of their equilibria. In particular, we prove guaranteed convergence to an equilibrium in the version which is closest to Schelling's original model. Moreover, we provide tight bounds on the Price of Anarchy.

Convergence and Hardness of Strategic Schelling Segregation

“…In the following section we analyze the convergence behavior of IRD for the strategic segregation process via swaps. Chauhan et al [11] already proved initial results in this direction, in particular that the SSG for two types of agents converges for the whole range of τ , i.e τ ∈ (0, 1), on ∆regular graphs and for τ ≤ 1 2 on arbitrary graphs. We close the gap and present a matching non-convergence bound in the SSG on arbitrary graphs.…”

“…They employ a utility function which depends on the type ratio in the neighborhood and which increases linearly with the fraction of agents of the own type in the neighborhood until a fraction of τ is reached. The authors of [11] investigate the convergence behavior of the induced sequential game for the cases where discontent agents are restricted either to performing only improving location swaps (called the Swap Schelling Game (SSG)) or where discontent agents are only allowed to jump to empty locations to improve on their situation (called the Jump Schelling Game (JSG)). This corresponds to analyzing IRD, whose analysis is also our main contribution.…”

“…An agent's aim is to find a node in the given network where she is content or, if this is not possible, where she has the highest possible positive neighborhood ratio. Therefore, and analogous to [11], we define the cost function of an agent a in a placement p G for network G as follows:…”

Schelling Games on Graphs

“…The model of Chauhan et al [2018] makes an important contribution to the literature by enriching Schelling's model with two additional components: agents who are fully strategic, and location preferences. However, the resulting model of agents' preferences is quite complex, and, consequently, not easy to analyze: the positive results in the paper are limited to special cases of the utility function and highly regular networks.…”

“…Specifically, just as in the work of Chauhan et al [2018], in our basic model the agents are partitioned into k types and the set of available locations is represented by an undirected graph, which we will refer to as the topology. We also incorporate location preferences in our model; however, instead of assuming that optimizing the distance to the preferred location is the secondary goal of every agent, we assume that agents are either stubborn, in which case they stay at their chosen location irrespective of their surroundings, or strategic, in which case they aim to maximize their happiness ratio by jumping to an unoccupied location (we do not consider swaps in this paper).…”