The hold-up literature shows how relationship-specific investments and incomplete contracts combine to hurt partnership profitability. (1) The conclusions typically build on the assumption that agents selfishly maximize own income. However, hold-up scenarios involve opportunistic exploitation. Intuition as well as a wealth of evidence suggest exploited parties may get irritated and strike back. It may seem such negative reciprocity can deter exploitation and render hold-up less problematic.
We explore the issue analytically and experimentally. We show that whether negative reciprocity mitigates hold-up depends predictably on the nature of the investment. Two contrasting examples (inspired by question 10 in chapter 5 of Besanko et al. 2010) illustrate the key principle involved:
EXAMPLE 1. An artist (player 1) has been asked by a presumptive buyer (player 2) to paint a "beautiful portrait of 2." 1 may disagree or agree. In the former case, 1 and 2 go separate ways. In the latter case, 1 spends $2,000 worth of his/her time on the painting, and a contract says 2 should subsequently pay $5,000 to 1. The value to 2 is $8,000, but 2 may complain and claim (falsely) that the portrait is "rather ugly" and attempt to renegotiate offering a new price of $1,000. Given the ambiguity of what constitutes beauty, 1 cannot enforce the $5,000 payment and will have to accept or reject the new offer. 1 knows that no person other than 2 would pay to acquire the painting.
Here, 2 could shoot himself in the foot by trying to renegotiate the price. 1 might become angry or, to use a phrase consistent with the intentions-based reciprocity theories of Rabin (1993) or Dufwenberg and Kirchsteiger (2004) (D&K), deem 2 unkind and desire to be unkind in return. 1 would then prefer to reject the renegotiated offer, and destroy (or disfigure and exhibit) the portrait. If 2 foresees this, then we have a case where negative reciprocity mitigates hold-up.
Our second example suggests that this insight only carries so far:
EXAMPLE 2. A professor (player 1) has been asked by a student (player 2) to extracurricularly teach 2 "how to use game theory to make a lot of money." 1 may disagree or agree. In the former case, 1 and 2 go separate ways. In the latter case, 1 spends $2,000 worth of his time talking to 2, and a contract says 2 should subsequently pay $5,000 to 1. The value to 2 is $8,000, but 2 may instead complain and claim (falsely) that the tutoring "was only good enough that he/she can make a moderate amount of money" and offer a renegotiated price of $1,000. Given the ambiguity of what is "a lot," 2 cannot enforce the $5,000 payment and he will have to accept or reject the new offer.
As strategic structure and monetary payoffs go, Example 2 may seem similar to Example 1. The sole difference is that if player 2 proposes to renegotiate the price, and if 1 rejects the offer, then 2 gains rather than loses. This reflects how education, unlike a portrait, comprises human capital which cannot be withheld. When players are vengeful this difference has repercussions for the entire strategic analysis. There is no way for player 1 to hurt player 2, therefore less to deter 2 from proposing a renegotiated price, and therefore less incentive for 1 to agree to the tutoring. Even if players are motivated by negative reciprocity, hold-up remains an issue. (2)
The key difference between Examples 1 and 2, however, is not whether a relation-specific investment concerns human capital. Rather, the issue concerns (to use a term of Grossman and Hart's 1986) who has "residual rights of control" of the proceeds of the investment. Human capital may be a prominent source of residual rights of control, but other sources are possible too. Say, to make things concrete, that we had an example (suggested by Ben Hermalin) with a home-owner and a plumber who installs a new system of pipes and drains in the homeowner's bathroom. …