Michael Crystal

Abstract: We study the problem of allocating a scarce good or service to individuals using a network to describe the allocative externalities among them. The policymaker seeks an allocation mechanism that maximizes agents’ total utilities, which equals the sum of private values and externalities. We show that this problem is NP-hard as it generalizes a version of the Max-Cut Problem with size restrictions. In cases where the policymaker has complete information on agents' values and externalities, we design an approximation algorithm that guarantees at least 75% of the optimal. This algorithm is based on a method of rounding linear relaxations and the connection to the Max-Cut problem. Additionally, we derive conditions under which allocating in a greedy manner is close to optimal. For scenarios in which the policymaker has no information, we provide a truthful-in-expectation (1-1/e)-approximation mechanism that is based on the convex rounding scheme presented at Dughmi (2011). Moreover, we analyze a simple (non-truthful) item bidding mechanism with VCG payments and show that there always exists an optimal pure strategy Nash equilibrium. We also provide efficiency guarantees for both pure strategy and Bayes-Nash equilibria.

Abstract: We present a framework for analyzing the near miss effect in lotteries. A decision maker (DM) facing a lottery, falsely interprets losing outcomes that are close to winning ones, as a sign that success is within reach. As a result of this false belief, the DM will prefer lotteries that induce a higher frequency of near misses, even if the underlying probability of winning is constant. We define a near miss index that measures the near miss effect induced by a given lottery and analyze the optimal lottery design in terms of near miss. This analysis leads us to establish a fruitful connection between our near miss framework and the field of coding theory. Building on this connection we compare different lottery frames and the near miss effect they induce. Analyzing an interaction between a seller and a buyer of lotteries allows us to gain further insight into the optimal framing of lotteries and might offer a potential explanation as to why lotteries with a very small probability of winning are commonplace and attractive.

We study the stability of social networks when agents are allowed to monitor the decisions of certain players to create or sever links within the network. Consider first the case where each agent can monitor their direct neighbors. A network is Peer-Monitored Stable if any unilateral deletion or mutual addition of a link negatively affects at least one neighbor. We prove that for two widely studied payoff structures, distance--based and degree--based, any Pareto--Efficient network is Peer-Monitored Stable.  We then extend our framework by allowing agents to monitor indirect connections within a defined radius of distance, introducing a measure of network stability based on the minimal level of monitoring required to stabilize the network. This measure provides a complete stability ranking over networks for which any single-link addition or deletion makes at least one agent worse off, with Pairwise Stable networks ranked as the most stable. Finally, we apply our measure to mixed externalities models and derive non-trivial upper bounds for the stability of Pareto-Efficient networks within the class of degree-distance-based payoffs.

Abstract: Patent citations have become an acceptable proxy for inventions’ quality. Our study offers the first systematic exploration of uncited patents. Analyzing data on all US patents issued between 1976 and 2008, we examine the ratio of uncited patents out of all patents granted each year. We find a robust pattern, consistent across technological fields, whereby the percentage of uncited patents declined between 1976 and the mid-1990s, but has been significantly increasing since then. We discuss policy implications of these findings and suggest that the ratio of uncited patents can serve as a complementary measure for evaluating the patent system.