  We study a model of competition among nomadic agents for time-varying and
location-specific resources, arising in crowd-sourced transportation services,
online communities, and traditional location-based economic activity. This
model comprises a group of agents and a single location endowed with a dynamic
stochastic resource process. Periodically, each agent derives a reward
determined by the location's resource level and the number of other agents
there, and has to decide whether to stay at the location or move. Upon moving,
the agent arrives at a different location whose dynamics are independent and
identical to the original location. Using the methodology of mean field
equilibrium, we study the equilibrium behavior of the agents as a function of
the dynamics of the stochastic resource process and the nature of the
competition among co-located agents. We show that an equilibrium exists, where
each agent decides whether to switch locations based only on their current
location's resource level and the number of other agents there. We additionally
show that when an agent's payoff is decreasing in the number of other agents at
her location, equilibrium strategies obey a simple threshold structure. We show
how to exploit this structure to compute equilibria numerically, and use these
numerical techniques to study how system structure affects the agents'
collective ability to explore their domain to find and effectively utilize
resource-rich areas.

Computer Science and Game Theory