Repeated interactions and endogenous contractual incompleteness

Let us mention that this result depends on our assumption about the strategy of the players, i.e., trigger strategy. This assumption is generally made in the literature about relational contracting (Baker et al. 1994, 2002; Levin 2002; Halac 2012). Yet, other strategies could lead to different equilibria.

Unforeseen contingencies can appear in \(j\le n\) contractual relationships.

A more general model showing that there is no pooling equilibrium and that each type of seller has no incentive to deviate to misrepresent as another type is provided in Desrieux and Beuve (2015). The intuition is that the type L seller gains nothing to postpone the decision to hold up in future, and the type H seller is always better off cooperating than deviating.

More formally, \(\delta =e^{-r\Delta }\) where r is the rate of time preference and \(\Delta \) is the length of the period. However, if we add a probability \(\mu \) of continuation from one period to the next, then with probability \((1-\mu )\) there is no gain, and with probability \(\mu \), the gain is discounted at rate \(\delta =e^{-r\Delta }\). Then, the expected discounted value of the gain is \(\delta '=\mu \delta =\mu e^{-r\Delta }\). Thus, the situation is the same as if \(\mu =1\) and \(r'=r-\frac{ln(\Delta )}{\mu }\), hence the dual interpretation of the discount rate.

An example of game instructions is provided in Appendix. Results of the control questionnaire: \(m=9.2/10\); \(\sigma \) 1.1. When at least one participant received a mark inferior than 5, we explained the rules of the game a second time.

Earnings in ECUs: \(m=583\), \(\sigma =182\). Earnings in Euros: \(m=14.6\), \(\sigma =4.6\). Duration of the session: between 15 and 30 minutes depending on treatments.

See Cochard et al. (2004) for an interesting study of the “reciprocity hypothesis” in repeated investment game.

It is important to note here that buyers cannot know which sellers are actually available on the market. At the beginning of each round, they can propose to any of the six sellers present in the lab without knowing if they are already engaged in three relationships. Such information would indeed act as a substitute for public information.

Before analyzing our results, we show that there is enough evidence to reject the proposition that samples of observations of our main variables are generated by the same stochastical process. The non-parametric Wilcoxon test reports are presented in Table 6 in the appendix.

The correlation matrix of all the variables used in the estimates is provided in Appendix; Table 10.

i.e., the number of cooperative choices divided by the number of incomplete contract situations in the past and in the relationship with a given buyer.

We use “Reputation” here as defined in Sect. (5.1.2).

This is consistent with our theoretical findings in Sect. 2. Cooperation is expected to be higher under public information. Since buyers adapt their investment regarding to past behavior of sellers, they should observe more cooperation and invest less in contractual completeness. However, the coefficient PublicInfo is only significant at the 10 % level, and we could have expected a stronger impact. This result may come from our restrictive theoretical assumptions (trigger strategy). In practice, other strategies can be chosen by the parties, so that the impact of PublicInfo is slightly weaker than we could expect. In addition, buyers may also get more incentives to invest in contractual completeness under public information, as they observe all sellers’ behavior. They know when they are associated with a non-cooperative seller and adapt their additional investment accordingly.

Similarly, we do not include interaction terms for collinearity reasons.

The measure of completeness adopted by Argyres et al. (2007) and Ryall and Sampson (2009) relies on the level of details (declared by contracting parties or observed though extensive document analysis) put into the contract, while Crocker and Reynolds (1993) describe contractual completeness through the pricing provisions (which defines the leeway of partners to adjust prices through time) adopted by the contracting parties.

Compared to the study of Crocker and Reynolds (1993), the experimental approach allows us to observe the entire story of relationships. History between parties start at the first period and the observed behaviors cannot be related to unobservable past events. Moreover, the empirical works as that of Crocker and Reynolds (1993) focus on relationships between one buyer and one or two sellers, while we can create in lab an environment where buyers and sellers are numerous and identically distributed in the population.