Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility

doi:10.1016/j.jet.2018.02.008

Journal of Economic Theory

Volume 177, September 2018, Pages 678-707

https://doi.org/10.1016/j.jet.2018.02.008 Get rights and content

Abstract

A fundamental result of modern economics is the conflict between efficiency and incentive compatibility, that is, the fact that some Pareto optimal (efficient) allocations are not incentive compatible. This conflict has generated a huge literature, which almost always assumes that individuals are expected utility maximizers. What happens if they have other kind of preferences? Is there any preference where this conflict does not exist? Can we characterize those preferences? We show that in an economy where individuals have complete, transitive, continuous and monotonic preferences, every efficient allocation is incentive compatible if and only if individuals have maximin preferences.

Introduction

One of the fundamental problems in mechanism design and equilibrium theory with asymmetric information is the conflict between efficiency and incentive compatibility. That is, there are allocations that are efficient but not incentive compatible. This important problem was alluded to in early seminal works by Wilson (1978), Myerson (1979), Holmstrom and Myerson (1983), and Prescott and Townsend (1984). Since incentive compatibility and efficiency are some of the most important concepts in economics, this conflict generated a huge literature and became a cornerstone of the theory of information economics, mechanism design and general equilibrium with asymmetric information.

It is a simple but perhaps important observation, that this conflict was predicated on the assumption that the individuals were expected utility (EU) maximizers, that is, they would form Bayesian beliefs about the type (private information) of the other individuals and seek the maximization of the expected utility with respect to those beliefs. Since the Bayesian paradigm has been central to most of economics, this assumption seemed natural.

The Bayesian paradigm is not immune to criticism, however, and many important papers have discussed its problems; e.g. Allais (1953), Ellsberg (1961) and Kahneman and Tversky (1979) among others. The recognition of those problems have led decision theorists to propose many alternative models, beginning with Bewley (1986, 2002), Schmeidler (1989) and Gilboa and Schmeidler (1989), but extending in many different models. For syntheses of these models, see Maccheroni et al. (2006) and Cerreia-Vioglio et al. (2011) among others.

The fact that many different preferences have been considered leads naturally to the following questions: Does the conflict between efficiency and incentive compatibility extend to other preferences? Is there any preference under which there is no such conflict? The purpose of this article is to answer these questions.

Our main result shows that all efficient (Pareto optimal) allocations are also incentive compatible if and only if individuals have (a special form of) the maximin expected utility (MEU) preferences introduced by Gilboa and Schmeidler (1989): Wald's maximin preference.¹ Therefore, the conflict between efficiency and incentive compatibility is much broader than previously established.

The implication that all efficient allocations are incentive compatible may suggest that the set of efficient allocations for maximin preferences is small, but we show that this is not the case. At least in the case of one-good economies, the set of efficient allocations under maximin preferences includes all allocations that are incentive compatible and efficient for EU individuals. This result (Theorem 5.1) seems somewhat surprising, since other papers have indicated that ambiguity may actually be bad for efficiency, limiting trading opportunities. See for instance Mukerji (1998) and related comments in section 6.

The paper is organized as follows. In section 2, we describe the setting and introduce definitions and notation. Section 3 presents the main result in the paper: all Pareto optimal allocations are incentive compatible if and only if all individuals are expected utility maximizers. We illustrate how our results can be cast in the mechanism design perspective in section 4. Section 5 establishes that the set of efficient and incentive compatible allocations in the EU setting are also MEU efficient. Section 6 reviews the relevant literature and section 7 discusses future directions of research. All proofs are collected in the appendix.

Section snippets

Model

Let $I = {1, . . ., n}$ be the set of individuals in the economy. Each agent $i \in I$ observes privately his own signal $t_{i}$ in some finite set of possible signals $T_{i}$ . Write $T = T_{1} \times \dots \times T_{n}$ . A vector $t = (t_{1}, . . ., t_{i}, . . ., t_{n}) \in T$ represents the vector of all types. As usual, $T_{- i}$ denotes $Π_{i \neq j}^{n} T_{j}$ and, similarly, $t_{- i}$ denotes $(t_{1}, . . ., t_{i - 1}, t_{t + 1}, . . ., t_{n})$ . We may write $t = (t_{i}, t_{- i})$ and, occasionally, we will write t as $(t_{i}, t_{j}, t_{- i - j})$ , with the obvious meaning.

Each individual cares about an outcome (e.g. consumption bundle) $b \in B = R_{+}^{L}$ ,

Main result

The central theme of this paper is the interplay of uncertainty, efficiency and incentive compatibility. To motivate our result, let us first discuss the conflict between efficiency and incentive compatibility that was noted in 70's.

Consider the following particular example. There are two individuals, with type sets $T_{1} = {U, D}$ and $T_{2} = {L, R}$ . Their utilities are $u_{i} (t, b) = b \in R_{+}$ , $\forall i \in I, t \in T$ and their endowments are constant and equal to 1: $e_{i} (t) = 1$ , $\forall i \in I, t \in T$ . Assume moreover that the individuals are

A mechanism design perspective

It is natural to ask what is the relevance of the above results from a mechanism design perspective. This section clarifies this issue. We begin by translating the usual mechanism design setting into our framework. The set of individuals and their information is exactly as we described before and there is a mechanism designer who wants to implement an efficient allocation. Instead of initial endowments, the mechanism design literature uses to consider only initial levels of utility, to inform

How do Bayesian and maximin efficiency compare?

From the fact that all maximin efficient allocations are incentive compatible, the reader may wonder whether maximin efficiency is an excessively strong requirement, which could explain (one direction of) our results. Indeed, if there are very few efficient allocations under maximin preferences, then the result that all of them are incentive compatible would be less compelling. In this section, we address this issue in particular cases. For one-good economies, we show that whenever an

General equilibrium with asymmetric information

It is well known that in a finite economy with asymmetric information once people exhibit standard expected utility, then it is not possible in general to find allocations which are Pareto optimal and also incentive compatible; see for an example the appendix. The key issue is the fact that, in a finite economy each agent's private information has an impact and therefore an agent will take advantage of this private informational effect to influence the equilibrium allocation to favor herself.

Concluding remarks and open questions

We showed that maximin preferences present no conflict between incentive compatibility and efficiency. We also showed that the maximin preferences are not only sufficient for any efficient allocation to be incentive compatible but they are also necessary. Additionally, this paper provides an axiomatization of the maximin preferences. Applications of our results to mechanism design were given. Finally, we applied our results to the Myerson–Satterthwaite's setup and showed that their negative

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^☆: The first version of this paper circulated in 2009, under the title “Ambiguity solves the conflict between efficiency and incentive compatibility”, when both authors were with the University of Illinois. We are grateful to Alain Chateauneuf, Huiyi Guo, Zhiwei (Vina) Liu, Marialaura Pesce, David Schmeidler, Marciano Siniscalchi and Costis Skiadas for helpful conversations. We also thank participants in many conferences and specially Subir Bose, who was a discussant of this paper on the Manchester Workshop in Economic Theory in 2010. The comments of two referees and Associate Editor are also gratefully acknowledged.

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Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility☆

Abstract

Introduction

Section snippets

Model

Main result

A mechanism design perspective

How do Bayesian and maximin efficiency compare?

General equilibrium with asymmetric information

Concluding remarks and open questions

Games Econ. Behav.

J. Econ. Theory

J. Math. Econ.

J. Public Econ.

Games Econ. Behav.

J. Math. Econ.

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

Le comportement de l'homme rationnel devant le risque: critique des postulats et axiomes de l'ecole americaine

Econometrica

Value allocation under ambiguity

Econ. Theory

Maximin, leximin and the protective criterion: characterizations and comparisons

J. Econ. Theory

Knightian Decision Theory. Part I

Knightian decision theory. Part I

Decis. Econ. Finance

Rational Decisions

Optimal auctions with ambiguity

Theor. Econ.

Mechanism design with ambiguous communication devices

Econometrica

Prudent expectations equilibrium in economies with uncertain delivery

Econ. Theory

General equilibrium in economies with uncertain delivery

Econ. Theory

Irrelevance of private information in two-period economies with more goods than states of nature

Econ. Theory

Ambiguity aversion and trade

Econ. Theory

Ambiguous implementation: the partition model

Econ. Theory

A New Perspective on Rational Expectations

An interpretation of Ellsberg's paradox based on information and incompleteness

Econ. Theory Bull.

The design of ambiguous mechanisms

Rev. Econ. Stud.

Risk, ambiguity, and the Savage axioms

Q. J. Econ.

Coping with ignorance: unforeseen contingencies and non-additive uncertainty

Econ. Theory

Objective and subjective rationality in a multiple prior model

Econometrica