Parallel Lotteries: Insights from Alaskan Hunting Permit Allocation

Abstract

We analyze the parallel lottery that is used to allocate hunting permits in the state of Alaska. Each participant is given 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 parallel lotteries approximate a competitive equilibrium from equal incomes (CEEI), which is Pareto efficient. When supply is moderate, parallel 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 giving applicants a suitable number of tickets k: trades are never beneficial when k = 1, and waste is eliminated as [Formula: see text]. In addition, we show that the wastefulness of the k-ticket parallel lottery has some benefits: agents with strong preferences may prefer parallel 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 parallel lottery performs well under most circumstances and may be suitable for other settings where items are rationed. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.