Strategic Resource Selection with Homophilic Agents

TL;DR

This work studies strategic resource selection among heterogeneous, homophilic agents by introducing Schelling Resource Selection Games with a threshold $\tau$ that governs the fraction of same-type users on a chosen resource. It develops two bounded-rationality models—impact-blind equilibria (IBE) and impact-aware equilibria (IAE)—and provides existence, computation, and approximation results for both, along with tight analyses of social-efficiency via Price of Anarchy and Price of Stability. The authors prove NP-hardness for social-welfare optimization in general, yet identify polynomial-time solutions for restricted instances and efficient algorithms to construct IBEs; IAEs exist for $\tau\le 1/2$ and admit potential-based proofs of convergence. The paper also establishes tight PoA bounds across all $\tau$ values, offers a 2-approximation to IAE for practical use, and discusses implications for real-world settings like school choice and residential segregation, highlighting the role of bounded information in producing stable, near-optimal outcomes.

Abstract

The strategic selection of resources by selfish agents is a classic research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then depends on the number of agents using the same resources. This implies that there is no distinction between the agents, i.e., they are anonymous. We depart from this very general setting by proposing Resource Selection Games with heterogeneous agents that strive for joint resource usage with similar agents. So, instead of the number of other users of a given resource, our model considers agents with different types and the decisive feature is the fraction of same-type agents among the users. More precisely, similarly to Schelling Games, there is a tolerance threshold $τ\in [0,1]$ which specifies the agents' desired minimum fraction of same-type agents on a resource. Agents strive to select resources where at least a $τ$-fraction of those resources' users have the same type as themselves. For $τ=1$, our model generalizes Hedonic Diversity Games with a peak at $1$. For our general model, we consider the existence and quality of equilibria and the complexity of maximizing social welfare. Additionally, we consider a bounded rationality model, where agents can only estimate the utility of a resource, since they only know the fraction of same-type agents on a given resource, but not the exact numbers. Thus, they cannot know the impact a strategy change would have on a target resource. Interestingly, we show that this type of bounded rationality yields favorable game-theoretic properties and specific equilibria closely approximate equilibria of the full knowledge setting.

Figures (3)

• Figure 1: Example instance of our model with three strategy profiles. The instance has two resources $q_1$ and $q_2$ (shown as circles, with their color fractions shown as pie charts), four red agents, and four blue agents, each shown as squares of the respective color. Moreover, we assume $\tau = \tfrac{3}{5}$. Accessibility is shown via edges, thick black edges show the chosen resource of the respective agent. The fractions below the squares show the utilities of the agents. (a) shows the social optimum strategy profile with a social welfare of $\tfrac{62}{15} > 4.1$. It is neither an IAE nor an IBE, since the blue agent highlighted in green can increase her utility from $\tfrac{2}{5}$ to $\tfrac{3}{5}$ by selecting resource $q_1$ instead of $q_2$. (b) shows an IAE. Since it has social welfare of $4.1$ it is not socially optimal. (c) depicts an IBE with social welfare of $4$. It is not an IAE, since changing to the respective other resource is an impact-aware improving move for all the green highlighted agents.
• Figure 2: Example instance from the proof of \ref{['poalower']} showing that the PoA bound in \ref{['poaupper']} is tight.
• Figure 3: Example instance from the proof of \ref{['thm:pos-not-one']} showing that the PoS is larger than $1$.

Theorems & Definitions (36)

• Theorem 1
• proof
• Corollary 1
• Theorem 2
• proof
• Theorem 3
• proof
• Lemma 1
• proof
• Lemma 2