Larry Samuelson

Managing Strategic Buyers

We consider the problem of a monopolist who must sell her inventory before some deadline, facing n buyers with independent private values. The monopolist posts prices but has no commitment power. The seller faces a basic trade-off between imperfect price discrimination and maintaining an effective reserve price. When there is only one unit and only a few buyers, the seller essentially posts unacceptable prices up to the very end, at which point prices collapse in a series of jumps to a reserve price that exceeds marginal cost. When there are many buyers, the seller abandons this reserve price in order to more effectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time.

Pricing in Matching Markets

Different markets are cleared by different types of prices---a universal price for all buyers and sellers in some markets, seller-specific prices that are uniform across buyers in others, and personalized prices tailored to both the buyer and the seller in yet others. We introduce the notion of premuneration values---the values in the absence of any muneration (payments)---created by the buyer-seller match. We characterize the premuneration values under which uniform-price and personalized-price equilibria agree. In this case, we have efficient allocations, including pre-match investment decisions, without the costs of personalized pricing. We then examine the inefficiencies that arise when the premuneration values preclude the agreement of uniform-price and personalized-price equilibria. We view premuneration valuesas an important consideration in market design.

What Really Matters in Designing School Choice Mechanisms

In the last decade, numerous student assignment systems have been redesigned using input from economists in the large American cities and elsewhere. This article reviews some of these case studies and uses practical experiences to take stock on what has really mattered in school choice mechanism design so far. While some algorithm design details are important, many are less practically important than initially thought. What really matters are basic issues that market operators in other contexts would likely be concerned about: straightforward incentives, transparency, avoiding inefficiency through coordination and well-functioning aftermarkets, and influencing inputs to the design, such as applicant decision-making and the quality of schools. INTRODUCTION In recent years, there has been a great deal of research activity and excitement among economists who study the design of systems used to assign students to schools. Motivated by Turkish college admissions, Balinski and Sonmez (1999) first defined the student placement problem, and Abdulkadiroglu and Sonmez (2003) defined the closely related school choice problem, motivated by K-12 public school admissions in the United States. Both articles showed how insights from matching theory could be used to re-engineer and potentially improve existing centralized school assignment systems. Abdulkadiroglu and Sonmez (2003) proposed two alternativemechanisms, which are adaptations of widely studied mechanisms in the literature on matching and assignment markets, following seminal contributions by Gale and Shapley (1962) and Shapley and Scarf (1974). Since that article was published, I have been involved in a number of efforts to redesign school choice systems, including those in New York City (2003), Boston (2005), New Orleans (2012), Denver (2012), Washington DC (2013), and Newark (2014). New systems have also been developed in England, Amsterdam, a number of Asian cities, and elsewhere. The purpose of this article is to review some facts from the field about these redesign efforts and to take stock on what I think has been important in practice so far. This article is not a survey of research on school choice market design (for surveys see, e.g., Pathak, 2011 and Abdulkadiroglu and Sonmez, 2013). My inspiration comes from Klemperer (2002), who presents his views on what matters for practical auction design based on his experience in designing auctions and advising bidders. Klemperer concludes that “in short, good auction design is mostly good elementary economics,” whereas “most of the extensive auction literature is of second-order importance for practical auction design.”

Analogies and Theories: Formal Models of Reasoning

The book describes formal models of reasoning that are aimed at capturing the way that economic agents, and decision makers in general think about their environment and make predictions based on their past experience. The focus is on analogies (case-based reasoning) and general theories (rule-based reasoning), and on the interaction between them, as well as between them and Bayesian reasoning. A unified approach allows one to study the dynamics of inductive reasoning in terms of the mode of reasoning that is used to generate predictions.

Learning, Experimentation, and Information Design

INTRODUCTION The purpose of this paper is to survey recent developments in a literature that combines ideas from experimentation, learning, and strategic interactions. Because this literature is multifaceted, let us start by circumscribing our overview. First and foremost, all surveyed papers involve nontrivial dynamics. Second, we will restrict attention to models that deal with uncertainty. Models of pure moral hazard, in particular, will not be covered. Third, we exclude papers that focus on monetary transfers. Our goal is to understand incentives via other channels – information in particular, but also delegation. Fourth, we focus on strategic and agency problems, and so leave out papers whose scope is decision-theoretic. However, rules are there to be broken, and we will briefly discuss some papers that deal with one-player problems, to the extent that they are closely related to the issues at hand. Finally, we restrict attention to papers that are relatively recent (specifically, we have chosen to start with Bolton and Harris, 1999). Our survey is divided as follows. First, we start with models of strategic experimentation. These are abstract models with few direct economic applications, but they develop ideas and techniques that percolate through the literature. In these models, players are (usually) symmetric and externalities are (mostly) informational. Moving beyond the exploitation/exploration trade-off, we then turn to agency models that introduce a third dimension: motivation. Experimentation must be incentivized. The first way this can be done (Section 3) is via the information that is being disclosed to the agent performing the experimentation, by a principal who knows more or sees more. A second way this can be done is via control. The nascent literature on delegation in dynamic environments is the subject of Section 4. Section 5 turns to models in which information disclosure is not simply about inducing experimentation, but manipulating the agents action in broader contexts. To abstract from experimentation altogether, we assume that the principal knows all there is to know, so that only the agent faces uncertainty. Finally, Section 6 discusses experimentation with more than two arms (Callander, 2011). EQUILIBRIUM INTERACTIONS Strategic Bandits Strategic bandit models are game-theoretic versions of standard bandit models. While the standard “multi-armed bandit” describes a hypothetical experiment in which a player faces several slot machines (“one-armed bandits”) with potentially different expected payouts, a strategic bandit involves several players facing (usually, identical) copies of the same slot machine.

BUYING LOCALLY: BUYING LOCALLY

Buy local arrangements encourage members of a community or group to patronize one another instead of the external economy. They range from formal mechanisms such as local currencies to informal Ill buy from you if you buy from me arrangements and are often championed on social or environmental grounds. We show that in a monopolistically competitive economy, buy local arrangements can have salutary effects even for selfish agents immune to social or environmental considerations. Buy local arrangements effectively allow firms to exploit the equilibrium price-cost gap to profitably expand their sales at the going price.

Reputations in Repeated Games, Second Version

This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information.

Economic Models as Analogies, Third Version

People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are theoretical cases, which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases.

Economic Models as Analogies, Second Version

People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are “theoretical cases”, which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice; why economists prefer simple examples; and why a paradigm may be useful even if it does not produce theories.

Cases and Scenarios in Decisions Under Uncertainty

We offer a model that combines and generalizes case-based decision theory and expected utility maximization. It is based on the premise that an agent looks ahead and assesses possible future scenarios, but may not know how to evaluate their likelihood and may not be sure that the set of scenarios is exhaustive. Consequently, she also looks back at her memory for past cases, and makes decisions so as to maximize a combined function, taking into account both scenarios and cases. We allow for non-additive set functions, both over future scenarios and over past cases, to capture (i) incompletely specified or unforeseen scenarios, (ii) ambiguity, (iii) the absence of information about counterfactuals, and (iv) some forms of case-to-rule induction (abduction) and statistical inference. We axiomatize this model. Learning in this model takes several forms, and, in particular, changes the relative weights of the two forms of reasoning.