Mediated audits

• DOI: http://doi.org/10.1111/1756-2171.12167
• Published date: 01 March 2017
• Author: Martin Pollrich
• Date: 01 March 2017

RAND Journal of Economics

Vol.48, No. 1, Spring 2017

pp. 44–68

Mediated audits

Martin Pollrich∗

I study optimal contracting where the principal can verify the agent’s private information via

auditing but cannot contractually commit to audit frequency. Optimal contracting requires so-

phisticated communication: the agent reports his informationto a mediator, who randomlyselects

a contract. Mediation allows for fine-tuning the information flow, because the principal observes

the selected contract but not the agent’s report.Simply offering a menu of contracts is, in general,

not optimal. I characterize optimal mediated contracts, determine conditions for when auditing

is profitable, and analyze contractual distortions. Mediated contracts can be implemented via

negotiated rulemaking procedures, and potentially via sequential communication.

1. Introduction

In a large class of economic interactions, an agent performs a task for a principal. Classical

examples include procurement of goods or services, regulated monopolies, or supplier-retailer

relationships. These interactions suffer from asymmetric information: typically, the agent has

private information, for instance, about costs of production or demand characteristics. Auditing

has proven effective in mitigating the frictions associated with informational asymmetries.1An

audit uncovers the agent’s private information ex post, thus rendering it less useful for him ex

ante. Much of the literature on auditing assumes the principal can commit to an audit policy,

implying in particular enforceability. However, optimal audit policies are usually not incentive

compatible.2Before an audit some information is revealed,for example, through the agent’schoice

∗Humboldt-Universit¨

at zu Berlin; martin.pollrich@hu-berlin.de.

For their helpful comments and suggestions, I thank Helmut Bester,Tilman B ¨

orgers, Yves Breitmoser, Franc¸oise Forges,

Paul Heidhues, Daniel Kr¨

ahmer, Matthias Lang, Gregory Pavlov, Frank Rosar, Roland Strausz, Peter Vida, as well as

seminar and conference audiences at Bergen, Berlin, Bonn, the 2013 Conference on Economic Design (Lund), the

2013 Stony Brook International Conference on Game Theory (Stony Brook), the 2014 European Winter Meeting of

the Econometric Society (Madrid), the 2015 Annual Conference of the European Association for Research in Industrial

Economics (Munich), the 2015 WorldMeeting of the Econometric Society (Montr ´

eal), the 2015 Conference on Auctions,

Competition, Regulation, and Public Policy(Lancaster), and the 20th Conference of the SFB/TR 15 (Bonn). This research

benefited from financial support by the German Science Foundationthrough SFB/TR 15 and RTG 1659, and from Einstein

Foundation Berlin through the Berlin Doctoral Program in Economics and Management Science. I am also grateful to

David Martimort (Editor) and two anonymous referees.

1See, e.g., Baron (1984), Baron (1989), Baron and Besanko (1984), Border and Sobel (1987), Demski, Sappington,

and Spiller (1987), Dunne and Loewenstein (1995), Graetz, Reinganum, and Wilde (1986), Hart (1995), Kofman and

Lawarr´

ee (1993), and Mookherjee and Png (1989).

2This has already been pointed out by Baron and Besanko (1984). Bolton and Scharfstein (1990), Hart (1995), and

Khalil and Lawarr´

ee (1995) elaborate more on this issue.

44 C2017, The RAND Corporation.

POLLRICH /45

of a contract, and given this additional information, a costly audit is not in the principal’s interest

anymore. Optimal audit policies are also difficult to enforce, either because they are random,

making it extremely difficult to monitor whether theprincipal adheres, or because it is impossible

to monitor whether the principal exerts any effort in auditing. Several authors address this issue,

but in the absence of a revelation principle, they have to impose restrictions on the contracting

game.3In general, the principal could devise arbitrarily complex sequential communication before

deciding upon a contract and whether to audit. The literature so far considers only a single stage

of communication, where only the informed party—the agent—talks.

In this article, I address these issues and derive the structure of optimal contracts in the

general framework, without relying on commitment to the audit policy and without restricting

communication. I study a canonical principal-agent model, where the agent produces a quantity

of a good for the principal. Marginal costs of production can be high or low and are the agent’s

private information. First, principal and agent communicate with each other. Next, they sign

a contract that determines the quantity to be produced, the agent’s compensation, and penalties

conditional on the (potential) audit finding. Finally, the principal can ask for an audit that uncovers

the agent’s true costs, but she cannot commit to the audit ex ante. The principal’s commitment

power is limited to developing rules for the communication and specifying a contract for each

outcome of this communication.

The principal would like to induce the agent to reveal some information during communica-

tion, because efficient production depends on the agent’s true costs. However, the principal will use

any information revealed early on when deciding whetherto audit. Having too much information

at that stage hampers incentives to audit, which adversely affects the agent’s incentives to reveal

that information in the first place. I show that the principal mitigates this tension by employing

a mediator for communication. More precisely, the agent reports his private information to the

mediator. Next, the mediator draws a contract depending on the agent’s report. After execution

of the contract, the principal decides whether to audit. The principal does not observe the agent’s

report to the mediator, and the agent cannot directly select a contract, but only a lottery over

contracts. The former reduces the information available to the principal when making the audit

decision to a bare minimum. The latter facilitates extraction of the agent’s private information.

To appreciate the value of mediation, it is worthwhile to reconsider the role of communica-

tion. In the simpler case of full commitment, that is, if the contract governs the entire allocation,

the revelation principle (e.g., Myerson, 1982) asserts that optimal communication is simple.4The

principal offers a menu of contracts from which the agent selects his preferred option. Moreover,

the optimal menu contains one contract for each type of agent, and each type always selects this

contract. Selecting a contract from a menu is akin for the agent reporting his type to the principal.

Yet, without commitment to the audit policy (in general, referred to as limited commitment),

neither of the above simplifications can be made without loss of generality. Providedthe principal

offers a menu of contracts, it may be beneficial if the agent randomizes. Khalil (1997) shows this

in an audit setting similar to the one in this article.5However, there is no justification for using

menu offers in the first place. After all, a menu offer is a convenient shortcut for asking the agent

to report his type to the principal. Alternatively, the principal can use more elaborate communi-

cation protocols such as multiple rounds of message exchange, communication via interested or

3These include Graetz, Reinganum, and Wilde (1986), Khalil and Lawarr´

ee (1995), Khalil (1997), Khalil and

Parigi (1998), Melumad and Mookherjee (1989), and more recently,Khalil and Lawarr´

ee (2006), Chatterjee, Morton, and

Mukherji (2008), and Lang and Wambach (2013).

4Both major textbooks on contract theory, Bolton and Dewatripont (2005), and Laffont and Martimort (2002),

almost exclusively deal with cases of full commitment.

5Bester and Strausz (2001) provide a more fundamental analysis of menu offers and randomization. They show

that if the agent chooses from a menu it is without loss that this menu contains one contract for each type of agent, and

that each type selects the designated contract with strictly positive probability—but not necessarily with prob.one.

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