Sequential Investment, Hold-Up, and Strategic Delay

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Sequential Investment, Hold-up, and Strategic Delay
Juyan Zhang∗ and Yi Zhang† December 20, 2010

Abstract We investigate hold-up with simultaneous and sequential investment. We show that if the encouragement effect of sequential complementary investments dominates the delay effect, sequential investment alleviates the underinvestment caused by the hold-up problem. Further, if it is allowed to choose when to invest, strategic delay occurs when the encouragement effect of sequential complementary investments dominates the delay effect. JEL classification: C70, D23 Keywords: Sequential Investment, Hold-up, Underinvestment, Strategic Delay

∗ †

Southwestern University of Finance and Economics; zhangjuyan@gmail.com. Singapore Management University; yizhang@smu.edu.sg.

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Introduction

According to Che and S´kovics (2008), “hold-up arises when part of the return on an a agents relationship-specific investments is ex post expropriable by his trading partner.” With incomplete contract, which arises due to causes such as unforeseen contingencies and inability of enforcement, relationship-specific investments are distorted by the hold-up problem and are therefore insufficient. The current literature on hold-up (see the survey of Che and S´kovics 2008) mainly a focuses on the inefficiency issue due to the hold-up problem and organizational or contract remedies to achieve the first best through some ex post renegotiation design. In their models, relationship-specific investments are usually simultaneously invested. In contrast, we investigate hold-up with simultaneous and sequential investment and focus on the impact of sequential investment on inefficiency issue of underinvestment. We show that if the encouragement effect of sequential complementary investments dominates the delay effect, sequential investment alleviates the underinvestment caused by the hold-up problem. Further, if it is allowed to choose when to invest, strategic delay occurs when the encouragement effect of sequential complementary investments dominates the delay effect. More specifically, there is a potentially profitable relationship between two parties. Some relationship-specific pre-investments from both sides are often involved, which is a double moral-hazard problem in terms of Laffont and Martimort (2002). The two parties have to rely on bargaining to divide the surplus of investment through the ex post renegotiation, since ex ante contracts are incomplete. With sequential investment, the leader may have incentive to invest more to elicit more investment from the follower – encouragement effect. Meanwhile, due to the delay of the realization of the surplus of investment under sequential investment – delay effect, sequential investment alleviates the underinvestment caused by the hold-up problem if the encouragement effect dominates the delay effect. Further, if parties have the option to choose when to invest, strategic delay occurs when the encouragement effect dominates the delay effect. Our model is close to Smironov and Wait (2004a, 2004b)’s sequential investment model. Smirnov and Wait (2004a, 2004b) provide a model to allow the flexibility in the timing of investment and show that the overall welfare may be detrimental due to the cost of delay. In their alternative investment regime (sequential investment), renegotiation occurs after the leader makes the relationship-specific investment and therefore there is no role of encouragement effect of sequential complementary investments. In contrast, in our model, contracting is impossible on both relationship-specific investments. Consequently, renegotiation will only occur after both relationship-specific investments are sunk.

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Our model is also related to the literature on property rights theory.1 N¨ldeke o and Schmidt (1998) and Zhang and Zhang (2010) show that the underinvestment caused by the hold-up problem still exists under the sequential investment setting. Further, Zhang and Zhang (2010) show the...
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