# Larry Samuelson Publications

## Abstract

A large literature uses matching models to analyze markets with two-sided heterogeneity, studying problems such as the matching of students to schools, residents to hospitals, husbands to wives, and workers to ﬁrms. The analysis typically assumes that the agents have complete information, and examines core outcomes. We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of complete-information stable outcomes. We provide suﬀicient conditions for incomplete-information stable matchings to be eﬀicient.

## Abstract

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rule-based reasoning. This uniﬁed framework allows us to examine, positively or normatively, how the various modes of inductive inference can be combined and how their relative weights change endogenously. We establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We show that even random data can make certain theories seem plausible and hence increase the weight of rule-based vs. case-based reasoning, leading the agent in some cases to cycle between being rule-based and case-based. We identify conditions under which minmax regret criteria will not be eﬀective.

## Abstract

Diﬀerent markets are cleared by diﬀerent types of prices — seller-speciﬁc prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market. We introduce the notion of premuneration values — the values to the transacting agents prior to any transfers — created by a buyer-seller match. Personalized price equilibrium outcomes are independent of premuneration values and exhibit ineﬀiciencies only in the event of “coordination failures,” while uniform-price equilibria depend on premuneration values and in general feature ineﬀicient investments even without coordination failures. There is thus a trade-oﬀ between the costs of personalizing prices and the ineﬀicient investments under uniform prices. We characterize the premuneration values under which uniform-price equilibria similarly exhibit ineﬀiciencies only in the event of coordination failures.

## Abstract

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 values as an important consideration in market design.

## Abstract

We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The agent’s actions are hidden, and the principal, who makes the oﬀers, cannot commit to future actions. We identify the unique Markovian equilibrium (whose structure depends on the parameters) and characterize the set of all equilibrium payoﬀs, uncovering a collection of non-Markovian equilibria that can Pareto dominate and reverse the qualitative properties of the Markovian equilibrium. The prospect of lucrative continuation payoﬀs makes it more expensive for the principal to incentivize the agent, giving rise to a dynamic agency cost. As a result, constrained eﬀicient equilibrium outcomes call for nonstationary outcomes that front-load the agent’s eﬀort and that either attenuate or terminate the relationship ineﬀiciently early.

## Abstract

We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The agent’s actions are hidden, and the principal, who makes the oﬀers, cannot commit to future actions. We identify the unique Markovian equilibrium (whose structure depends on the parameters) and characterize the set of all equilibrium payoﬀs, uncovering a collection of non-Markovian equilibria that can Pareto dominate and reverse the qualitative properties of the Markovian equilibrium. The prospect of lucrative continuation payoﬀs makes it more expensive for the principal to incentivize the agent, giving rise to a dynamic agency cost. As a result, constrained eﬀicient equilibrium outcomes call for nonstationary outcomes that front-load the agent’s eﬀort and that either attenuate or terminate the relationship ineﬀiciently early.

## Abstract

We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The repeated interaction gives rise to a dynamic agency cost — the more lucrative is the agent’s stream of future rents following a failure, the more costly are current incentives for the agent, giving the principal an incentive to reduce the continuation value of the project. We characterize the set of recursive Markov equilibria. We also ﬁnd that there are non-Markov equilibria that make the principal better oﬀ than the recursive Markov equilibrium, and that may make both agents better oﬀ. Eﬀicient equilibria front-load the agent’s eﬀort, inducing as much experimentation as possible over an initial period, until making a switch to the worst possible continuation equilibrium. The initial phase concentrates the agent’s eﬀort near the beginning of the project, where it is most valuable, while the eventual switch to the worst continuation equilibrium attenuates the dynamic agency cost.

## Abstract

We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The repeated interaction gives rise to a dynamic agency cost — the more lucrative is the agent’s stream of future rents following a failure, the more costly are current incentives for the agent, giving the principal an incentive to reduce the continuation value of the project. We characterize the set of recursive Markov equilibria. We show that there are non-Markov equilibria that make the principal better oﬀ than the recursive Markov equilibrium, and that may make both players better oﬀ. Eﬀicient equilibria front-load the agent’s eﬀort, inducing as much experimentation as possible over an initial period, until making a switch to the worst possible continuation equilibrium. The initial phase concentrates the agent’s eﬀort near the beginning of the project, where it is most valuable, while the eventual switch to the worst continuation equilibrium attenuates the dynamic agency cost.

## Abstract

This paper examines circumstances under which subjectivity enhances the eﬀectiveness of inductive reasoning. We consider a game in which Fate chooses a data generating process and agents are characterized by inference rules that may be purely objective (or data-based) or may incorporate subjective considerations. The basic intuition is that agents who invoke no subjective considerations are doomed to “overﬁt” the data and therefore engage in ineﬀective learning. The analysis places no computational or memory limitations on the agents — the role for subjectivity emerges in the presence of unlimited reasoning powers.

## Abstract

We consider the problem of a monopolist with an object to sell before some deadline, facing *n* buyers with independent private values. The monopolist posts prices but has no commitment power. We show that the monopolist can always secure at least the larger of the static monopoly proﬁt and the revenue from a Dutch auction with a zero reserve price. When there are only a few buyers, her proﬁts are higher than this bound, and she essentially posts unacceptable prices up to the very end, at which point prices collapse to a “reservation price” that exceeds marginal cost. When there are many buyers, the seller abandons this reservation price in order to more eﬀectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time. With more units to sell, prices jump up after each sale.

## Abstract

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.

## Abstract

Psychologists report that people make choices on the basis of “decision utilities” that routinely overestimate the “experienced utility” consequences of these choices. This paper argues that this dichotomy between decision and experienced utilities may be the solution to an evolutionary design problem. We examine a setting in which evolution designs agents with utility functions that must mediate intertemporal choices, and in which there is an incentive to condition current utilities on the agent’s previous experience. Anticipating future utility adjustments can distort intertemporal incentives, a conflict that is attenuated by separating decision and experienced utilities.