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2 - Learning, Experimentation, and Information Design
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- By Johannes Hörner, Yale University, Andrzej Skrzypacz, Stanford University
- Edited by Bo Honoré, Princeton University, New Jersey, Ariel Pakes, Harvard University, Massachusetts, Monika Piazzesi, Stanford University, California, Larry Samuelson, Yale University, Connecticut
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- Book:
- Advances in Economics and Econometrics
- Published online:
- 27 October 2017
- Print publication:
- 02 November 2017, pp 63-98
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Summary
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 agent's 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.
6 - Comments on “Contracts”
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- By Johannes Hörner, Yale University
- Edited by Daron Acemoglu, Massachusetts Institute of Technology, Manuel Arellano, Eddie Dekel
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- Book:
- Advances in Economics and Econometrics
- Published online:
- 05 May 2013
- Print publication:
- 13 May 2013, pp 172-176
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Summary
The theory of contracts was surveyed at a previous Econometric Society World Congress by Oliver Hart and Bengt Holmström (1985). Their masterful survey correctly predicted a major theme that would dominate contract theory in the following decade – namely, incompleteness (Tirole, 1999). Indeed, the two leading textbooks on contract theory both conclude their exposition on this topic (Bolton and Dewatripont 2005; Salanié 2005). Yet, readers would look in vain for this word in the chapters of this volume by Bruno, Thomas, Jean-Charles, and Yuliy. Not once does incompleteness appear and it is hardly mentioned in the recent flurry of papers on the topic that they discuss. What unforeseen contingency has “pumped new blood” into contract theory?
A striking and common feature of these chapters is their technical sophistication. Many – if not most – adopt a continuous-time framework in which output or cash flows are modeled as diffusions: typically, a Brownian or a Poisson process, the drift or jump intensity of which the agent controls. Such modeling offers several benefits.
Before discussing them, I first want to clear up any misunderstanding regarding what the framework does not offer so far. In my view, our understanding of the fundamental properties of optimal contracts under repeated moral hazard, as well as of its basic representation, has hardly evolved since the pioneering work of Rogerson (1985) and Spear and Srivastava (1987). To be sure, the work of Yuliy, for instance (see his Proposition 1), offers an enlightening new take on their characterizations; however, what it gains in elegance, it loses in generality. Microeconomic theorists on a quest for absolute truths are likely to balk at the restrictions for which such models invariably call, although these theorists might be the ones most likely to succumb to the sirens of their mathematical beauty.