Mean Field Equilibria for Competitive Exploration in Resource Sharing Settings

TL;DR

This paper models strategic agents exploring dynamic resources in shared locations, establishing the existence of threshold-based equilibria in large systems, which helps understand collective exploration and resource utilization.

Contribution

It introduces a mean field equilibrium model for competitive exploration with dynamic resources, revealing a threshold structure in large agent-location systems.

Findings

Existence of equilibrium with threshold structure

Agents' decisions depend on local resource levels and agent density

Insights into how system parameters influence exploration efficiency

Abstract

We consider a model of nomadic agents exploring and competing for time-varying location-specific resources, arising in crowdsourced transportation services, online communities, and in traditional location based economic activity. This model comprises a group of agents, and a set of locations each endowed with a dynamic stochastic resource process. Each agent derives a periodic reward determined by the overall resource level at her location, and the number of other agents there. Each agent is strategic and free to move between locations, and at each time decides whether to stay at the same node or switch to another one. We study the equilibrium behavior of the agents as a function of dynamics of the stochastic resource process and the nature of the externality each agent imposes on others at the same location. In the asymptotic limit with the number of agents and locations increasing proportionally, we show that an equilibrium exists and has a threshold structure, where each agent decides to switch to a different location based only on their current location's resource level and the number of other agents at that location. This result provides insight into how system structure affects the agents' collective ability to explore their domain to find and effectively utilize resource-rich areas. It also allows assessing the impact of changing the reward structure through penalties or subsidies.