Equilibrium and optimal one-shot delegated search

A target is located at one of m given sites, with known probabilities. Each of a set of searchers selects a site to search, and a fixed prize is shared by those who search the correct location. What (symmetric) search strategies are adopted when the searchers act selfishly to maximize their expected returns, and how can a firm affect this behavior to increase the efficiency of the search? This is a common situation when, for example, a firm faces a time-limited business opportunity. To materialize it the firm must solve a design problem that it delegates to a limited number of experts, and sets up a contest in order to motivate them to search for the solution. The firm is interested in maximizing the probability that the problem is solved by at least one of the searchers. Other applications include mathematical contests, innovation contests, and “guess & win” contests. We investigate the searchers’ incentives and how they conform with the firm’s goal. We analyze the equilibrium selection strategies and the strategies that maximize the probability that the search is successful and the target is discovered by at least one searcher. We show that selfish (equilibrium) search leaves too many sites unsearched while searching excessively the high-probability locations. We analyze the relative loss caused when the equilibrium search strategy is applied rather than the optimal one, and show that even with just two sites, it can be as large as 20%. We present two methods for inducing the optimal strategy in equilibrium, one uses heterogeneous prizes while the other one does not use direct monetary incentives. Awareness of the gap between agents’ incentives and firm’s goals should direct a principal when deciding whether it is desirable to delegate the search for a design problem, and if so then how to provide adequate incentives.