Alaskan Hunting License Lotteries are Flexible and Approximately Efficient

Abstract

We analyze the k-ticket lottery, which is used to allocate hunting permits in the state of Alaska. Each participant is given k tickets to distribute among lotteries for different types of items. Participants who win multiple items receive their favorite, and new winners are drawn from the lotteries with unclaimed items.

When supply is scarce, equilibrium outcomes of the k-ticket lottery approximate a competitive equilibrium from equal incomes (CEEI), which is Pareto efficient. When supply is moderate, k-ticket lotteries exhibit two sources of inefficiency. First, some agents may benefit from trading probability shares. Second, outcomes may be ``wasteful": agents may receive nothing even if acceptable items remain unallocated. We bound both sources of inefficiency, and show that each is eliminated by a suitable choice of k: trades are never beneficial when k = 1, and waste is eliminated as k approaches infinity.

The wastefulness of the k-ticket lottery has some benefits: agents with strong preferences may prefer k-ticket lottery outcomes to those of any nonwasteful envy-free mechanism. These agents prefer small values of k, while agents with weak preferences prefer large values of k. Together, these results suggest that the k-ticket lottery performs well under most circumstances, and may be suitable for other settings where items are rationed.

Keywords: matching, market design, allocation without money, competitive equilibrium from equal incomes

JEL Classification: D45, D47, C78