Trade-Offs Between Information and Crowding in Sequential Decisions (Student Abstract)

A rich line of theoretical work has modeled scenarios in which a set of agents make decisions sequentially, based on observing a growing mix of public and private signals that are revealed as these decisions occur. Here, we study a second crucial dimension, which is the way in which strategies can depend on crowding. In particular, consider a setting in which agents must sequentially decide which of several options to invest in, each based on a public signal that they receive. One of these options will ultimately be revealed to be valuable; but crucially, all the agents who selected this option must divide the value that comes from it. As a result, when a given agent j goes to make a decision among the options, the decisions of earlier agents convey information about the payoff that j will receive in any eventual division of the value. When many earlier agents have chosen a specific option, the greater crowding on this option means it must be divided more finely, resulting in lower payoffs. To simulate large games when signals are public, we define a polynomial-time algorithm to compute equilibrium strategies. We show that even in this case of public signals, the interaction of crowding with informational effects leads to complex non-monotonicities in the resulting sequential decisions, with agents sometimes choosing options with lower expected levels of crowding --- and hence a better split of the potential value --- over options with better informational or current crowding properties.