  We consider the information design problem in spatial resource competition settings. Agents gather at a location deciding whether to move to another location for possibly higher level of resources, and the utility each agent gets by moving to the other location decreases as more agents move there. The agents do not observe the resource level at the other location while a principal does and the principal would like to carefully release this information to attract a proper number of agents to move. We adopt the Bayesian persuasion framework and analyze the principal's optimal signaling mechanism design problem. We study both private and public signaling mechanisms. For private signaling, we show the optimal mechanism can be computed in polynomial time with respect to the number of agents. Obtaining the optimal private mechanism involves two steps: first, solve a linear program to get the marginal probability each agent should be recommended to move; second, sample the moving agents satisfying the marginal probabilities with a sequential sampling procedure. For public signaling, we show the sender preferred equilibrium has a simple threshold structure and the optimal public mechanism with respect to the sender preferred equilibrium can be computed in polynomial time. We support our analytical results with numerical computations that show the optimal private and public signaling mechanisms achieve substantially higher social welfare compared with no information or full information benchmarks in many settings. 
Information Design in Spatial Resource Competition