Information and bargaining in the hold-up problem.

This article incorporates an information structure with partial information into the canonical hold-up problem. The optimal information structure balances the tradeoff between ex ante efficiency (the "information rent" effect) and ex post efficiency (the "bargaining disagreement" effect). With one-shot bargaining, it occurs at an intermediate level of information asymmetry; when there is repeated bargaining, it is attained with perfect asymmetry. Asymmetric information, the parameter that is frequently ignored in the literature, turns out to be an important welfare instrument for the hold-up problem. Our results therefore provide a basis for institutional design regarding the optimal control of information flow.

1. Introduction

* In their influential paper, Klein, Crawford, and Alchian (1978) explain vertical integration in terms of reducing transactions costs for "post-contractual opportunistic behavior." Since this seminal contribution, there has been an extensive literature attempting to account for existing economic institutions based on a fundamental phenomenon: the hold-up problem. When one party transacts with another, it often involves some relationship-specific investment. Because contracts are incomplete, these parties have to rely on bargaining to divide the surplus of investment. Typically, however, the agent who makes this ex ante investment is not its residual claimant because she does not have all the bargaining power at the ex post bargaining stage. Knowing that her sunk investment cost will not be fully compensated, she therefore underinvests. Despite the widespread study of this classic problem and the presence of information asymmetry in virtually every economic situation, "[a]symmetric information has played a very limited role in the analysis of the hold-up problem" (Hart, 1995). In the bulk of the existing incomplete-contract literature initiated by Grossman and Hart (1986) and Hart and Moore (1988), all the variables of interest are assumed to be observable at the bargaining stage. Therefore, ex post efficiency is automatically guaranteed and any inefficiency comes from ex ante underinvestment. Such a simplifying assumption is particularly problematic considering the emphasis of human capital investment in the literature. Even if investment is purely physical, its degree of specificity may still be private knowledge.

Recently, asymmetric information has started to appear in the literature, most notably Gibbons (1992) and Gul (2001). (1) They study the classic hold-up problem in which the investor has no bargaining power in the one-shot bargaining game that follows. As expected, this complete lack of bargaining power translates into a complete lack of investment incentives. They then ask what happens when the investment decision is not observable. In fact, the joint surplus is exactly the same with or without observability. Like other papers incorporating asymmetric information into the hold-up problem, however, they both assume either full information or no information.

In contrast, this article studies the hold-up problem under partial information, which is a more realistic description of most situations. Our model consists of a risk-neutral buyer who is interested in buying a single unit of a product. She makes a costly investment that deterministically increases her value of the item. With some probability, the investment is observed by the seller, who is also risk neutral. The seller then makes a take-it-or-leave-it offer. By varying the probability of observability, we characterize explicitly the various effects of asymmetric information on the hold-up problem and the sensitivity of its equilibrium outcome. It might be tempting to generalize from the results of Gibbons (1992) and Gul (2001) that any degree of information asymmetry necessarily leads to the same welfare level. We show that the parties' joint surplus in fact varies non-monotonically with the degree of information asymmetry. The key observation is that asymmetric information introduces two counterbalancing forces. It increases disagreement at the bargaining stage but, because the information rents strengthen investment incentives, underinvestment is reduced. Within a wide range of information structures, the joint surplus is strictly greater than that under either full information or no information. Put differently, the optimal information structure occurs at the interior. Therefore, it can be misleading to just look at the two polar cases.

Indeed, in some situations, bargaining does not end after a one-shot attempt. Yet, repeated bargaining does not improve the joint surplus at all, as long as there is full observability. More strikingly, Gul (2001) goes further to show that unobservability, together with repeated bargaining, does solve the hold-up problem completely: the parties attain the first-best outcome in the limit, as the time between successive offers goes to zero. Recognizing the requirement of unobservability may be unrealistic in this context, he further conjectures that "a small amount of asymmetric information between the buyer and the seller regarding the buyer's investment level may be sufficient" to achieve this socially efficient outcome.

We extend our partial-information hold-up model to infinite-horizon bargaining by letting the seller make repeated offers. This extension also allows us to look at the interactions between the negative "bargaining disagreement" and the positive "information rent" effects in a dynamic context. With repeated bargaining, "bargaining disagreement" is replaced by "bargaining delay." Recall the seller always extracts the whole surplus in one shot whenever the true investment is observed. As the time between successive offers goes to zero, any delay is essentially killed off also when investment is not observed. The buyer therefore becomes the "information-truncated" residual claimant to her investment. Consequently, her investment incentives and hence the joint surplus improve unambiguously with a higher degree of information asymmetry. Nevertheless, the first-best outcome can be achieved only under the extreme case of perfect information asymmetry.

As a byproduct, our results demonstrate that the possibility of repeated bargaining is always desirable.

We further endogenize the information structure by allowing the seller to carry out costly information acquisition. In the more realistic scenario when he cannot commit to a particular information structure, there is always overacquisition relative to what is socially optimal. Nevertheless, an intermediate level of information asymmetry emerges endogenously in equilibrium, confirming the robustness of our previous results.

The central message of this article is that asymmetric information, the parameter that has been frequently ignored in the literature, turns out to be an important welfare instrument for the hold-up problem. Its implications are twofold. First, our results provide a basis for institutional design regarding the optimal control of information flow. Moreover, because the optimal information structure depends crucially on whether bargaining is one shot or repeated, use of this instrument should depend on the situation considered. In particular, if the good being traded is perishable or short-lived and there is no room for repeated bargaining, then the optimal institution will involve an intermediate degree of information asymmetry. On the other hand, where repeated bargaining is viable, it will be desirable to ensure its feasibility and limit information flow to the greatest possible extent.

One theoretical advantage of our model is that it concerns information flow between firms. In contrast, the property rights models based on the authoritative work of Grossman and Hart (1986) and Hart and Moore (1990) propose solving the hold-up problem using integration or disintegration, while ignoring the (potentially large) impacts such a restructuring might have on the internal organization and incentives within each firm. In a world in which most firms consist of multitiers and agency problems are abundant, it is hard to justify that their internal organization and incentives will remain intact after a merger or an acquisition. This point has been emphasized by Bolton and Scharfstein (1998) and Holmstrom and Roberts (1998).

In practice, the control of information flow between firms can be achieved, for example, by adjusting the relevant disclosure laws. In some sense, our results also contribute to the disclosure literature. As Dye (2001) points out, several important classes of disclosure models give extreme predictions regarding the optimal level of disclosure. This article, in contrast, provides a rationale for the optimality of partial disclosure, which is more consistent with empirical observations.

The rest of this article is organized as follows. Section 2 describes the main model, followed by its analysis in Section 3. Sections 4 and 5 modify the basic model to accommodate repeated bargaining and information acquisition, respectively. Finally, Section 6 concludes this article. All proofs are relegated to the Appendix.

2. The partial-information hold-up model