Resource Allocation with Population Dynamics

TL;DR

This paper introduces a general behavioral model for resource allocation involving a heterogeneous population governed by a Markov chain, demonstrating convergence under certain conditions and broad applicability of the methods.

Contribution

It presents a novel, more realistic population dynamics model for resource allocation problems and proves convergence results using new analytical techniques.

Findings

Distribution of agents converges in distribution under certain conditions

Model generalizes previous simplistic population models

Proof techniques have potential for wider application

Abstract

Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the evolution of a heterogeneous population of agents is governed by a Markov chain. Still, we are able to show that the distribution of agents across resources converges in distribution, for suitable means of information provision, under certain assumptions. The model and proof techniques may have wider applicability.