Information control in the hold‐up problem

• Author: Teck Yong Tan,Anh Nguyen
• DOI: http://doi.org/10.1111/1756-2171.12295
• Published date: 01 December 2019
• Date: 01 December 2019

RAND Journal of Economics

Vol.50, No. 4, Winter 2019

pp. 768–786

Information control in the hold-up problem

Anh Nguyen∗

and

Teck Yong Tan∗∗

Westudy the use of information control to mitigate hold-up risks. We identify a distinction between

asymmetric information that creates an ex ante investmentincentive and asymmetric information

that causes ex post inefficiency, which then allows ex post inefficiency to be eliminated without

compromising the ex ante investment incentive. We characterize the properties of the optimal

information structure and the payoffs and welfare achievable with information control in the

presence of hold-up risks.

1. Introduction

This article revisits the classic hold-up problem: an economic agent has the opportunity

to make a costly and sunk investment that increases the surplus of a potential partnership,

but anticipating that his partner would alter the terms of the partnership and expropriate the

gains from the investment later, the agent chooses not to invest in the first place. Such hold-

up risks are ubiquitous in many situations, including relationship-specific investment in joint

business ventures, acquisition of firm-specific skills by employees, provision of general training

by firms, campaign contributions in political lobbying, and quality investment by hospitals in the

healthcare market.

Some articles (e.g., Gul, 2001; Lau, 2008) have suggested that hold-up risks could potentially

be mitigated by hiding the investment from the partner. The resulting asymmetric information

limits the partner’s ability to extract the investment gains, thus improving ex ante efficiency by

partially restoring the investingagent’sinvestment incentive. However, ex post inefficiency can also

arise when the parties negotiate the terms of the partnership under asymmetric information. This

suggests that a trade-off exists between creating an ex ante investment incentive and minimizing

∗Carnegie Mellon University; anhnguyen@cmu.edu.

∗∗Nanyang Technological University; teckyongtan@ntu.edu.sg.

We are grateful to the Editor and three anonymous referees for helpful comments and suggestions. We thank Charles

Angelucci, Yeon-Koo Che, Navin Kartik, Kate Ho, Johannes H¨

orner, Mike Riordan, Tobias Salz, Bernard Salani´

e, Ran

Spiegler, and seminar and conference participants at Carnegie Mellon University, Columbia University, University of

Pittsburgh, the Asian Meeting of the Econometric Society 2018 (Seoul), IIOC 2019 (Boston), and SAET 2018 (Taipei)

for their useful feedback.

768 C2019, The RAND Corporation.

NGUYEN AND TAN / 769

ex post inefficiency, and the optimal information control must balance the two effects.1Our

goals in this article are to show that this trade-off is not necessary under more general forms

of information control and to distinguish asymmetric information that generates an ex ante

investment incentive from asymmetric information that causes ex post inefficiency.

As an example, consider a relationship between an upstream supplier whosupplies inputs for

the production process of a downstream manufacturer. The supplier could make manufacturer-

specific investments that lower its cost to produce the inputs; however, as the quality and type

of investment are difficult to verify, the parties cannot write contracts that are contingent on the

supplier’s investment, which generates hold-up risks. Nevertheless, the two parties are often able

to contract on the terms that govern the manufacturer’s ability to inspect the supplier’s facilities,

such as the frequency and areas of inspection.2In turn, these terms affect the probability that

the manufacturer can learn about the supplier’s investment, and we show that when appropriately

designed, these terms can improve the supplier’s investment incentive without incurring any

post-investment “haggling” cost.

We follow the related literature and frame the hold-up problem throughout this article in

a monopoly setting where a buyer (he) can make an uncontractible investment to increase his

valuation for a good sold by a monopolist seller (she). We add to this setup a signal structure that

generates signals to the seller regarding the buyer’s eventual valuation. To see how information

control can disentangle the effects of different types of asymmetric information, notice that the

buyer’s ex ante investment incentive comes from the seller being (at least sometimes) unaware of

the buyer’s higher valuation and undercharging him—this concerns hiding information from the

seller in the “investment state.” On the other hand, ex post inefficiency from a trade breakdown

arises when the seller is unaware of the buyer’s low valuation and still charges a high price—this

concerns hiding information about the “noninvestment state,” which does not affect the buyer’s

investment incentive. In turn, we can exploit this distinction to eliminate ex post inefficiency

while maintaining the buyer’s investment incentive.

Our analysis begins by showing that when the seller cannot directly observe the investment,

the buyer’s investment decision must be randomized in equilibrium. This is readily understood

under binary investment: if the seller anticipates that the buyer always invests, she will charge

a high price, which destroys the buyer’s ex ante investment incentive; on the other hand, if she

anticipates that the buyer never invests, she will charge a low price, which then induces the

buyer to invest. A stochastic investment strategy implies that the first best is not achievable by

information control, but we show that it can still always improve welfare relative to a complete

hold-up, which arises when the seller perfectly observes the investment.

To simplify the problem, we first derive a technical result that allows us to, without loss of

generality, restrict our attention to “direct” signal structures making incentive-compatible price

recommendations to the seller. Although this is straightforward from the revelation principle on

the seller’s side, the novelty lies in showing that direct signal structures can preserve the buyer’s

investment incentive, which is based on the signal structure as a whole.

Our aim is to characterize the set of investment probabilities and social welfare that are

sustainable in equilibrium and the signal structures that implement them. In general, the buyer’s

investment incentive comes from the seller being too pessimistic about the buyer’s valuation and

undercharging him, whereas an ex post trade breakdown occurs when the seller is too optimistic

and overcharges the buyer. Pessimism (respectively, optimism) arises when the signal structure

muddles information about the buyer’s true investment with signals that suggest lower (respec-

tively, higher) investments. Given this separation, the optimal signal structure is characterized by

1As Lau (2008) wrote in her abstract, “The optimal information structure balances the tradeoff between ex ante

efficiency (the “information rent” effect) and ex post efficiency (the “bargainingdisag reement” effect).”

2See, for example, Smith (2007) for an expositionon including clauses on auditing the variousaspects of production

in contracts for outsourcing.

C

The RAND Corporation 2019.