  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.
