Title: Lotteries for Shared Experiences (joint work with Carlos Bonet)
Abstract: We consider a setting where tickets for an experience are allocated by lottery. Each agent belongs to a group, and cares not only about her own allocation, but also about the allocation of other members of her group. In particular, a group is successful if and only if its members receive enough tickets for everyone to participate. We say that a lottery is efficient, when it maximizes the number of agents in successful groups, and fair, when it gives every group the same chance of success. An ideal lottery would be simultaneously efficient and fair. We study the efficiency and fairness of three mechanisms. The most widespread mechanism is the Individual Lottery. In it, each agent chooses a number of tickets to request. Then agents are ordered uniformly at random and sequentially allocated tickets until none remain. We discuss two deficiencies of this mechanism: (i) large groups have a significant advantage over small groups, and (ii) multiple members from a group may be awarded, resulting in wasted tickets. We show that these issues may lead to arbitrarily unfair and inefficient outcomes. One alternative is the Group Lottery: agents report their groups, then groups are ordered uniformly at random and sequentially allocated tickets until none remain. This mechanism corrects both deficiencies above, and therefore is approximately fair and approximately efficient. However, it requires verifying identities of each group member, which may be too cumbersome for many applications. Finally, we introduce the Weighted Individual Lottery. This is an Individual Lottery biased against agents with large requests. Although it's still possible to have multiple winners in a group, this simple modification drastically reduces the chance of this happening. As a result, this mechanism is approximately fair and approximately efficient, and similar to the Group Lottery when there are many more agents than tickets.
Bio: Nick Arnosti is an Assistant Professor at Columbia Business School, where he teaches the MBA core class Operations Management, as well as a PhD elective on Rationing Social Goods. He received a PhD in Operations Research from Stanford University in 2016 (advised by Ramesh Johari and Paul Milgrom). His research focuses on market design, with particular emphasis on giving away social goods such as affordable housing and public school seats. He has also studied the allocation of hunting licenses, hiking permits, and discounted tickets to events.
