Albin Erlanson, Department of Economics (Stockholm)

Optimal allocations with capacity constrained verification. Job Market Seminar

Abstract:

There is a principal with m identical objects to allocate among a group of n agents. Objects are desirable and each agent needs at most one copy. Assigning an object to agent i generates a value of t_i to the principal and the principal’s objective is to maximize the expected value from allocating the m objects. Agent i’s type t_i is his private information. There are no monetary transfers available but the principal can verify up to k agents, where k<m, upon which he perfectly learns the verified agent’s type. The principal can penalize a lying agent by not assigning him an object. We find the optimal mechanism to allocate the m objects. This mechanism asks agents to report their type and divides the type space into three different intervals. An agent with a report in the highest interval is assigned an object if he is among the m highest reports. An agent with a report in the middle interval is assigned an object with certainty if he is among the k highest reports, otherwise he takes part in a lottery for any remaining objects when there are less than m reports in the highest interval. Any report in the lowest interval has the same positive expected probability of winning an object. The verification rule is chosen so that truthful reporting is an equilibrium.

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