6. Incomplete Information

Both situations concern so-called one-sided asymmetric information. This means one of the parties has more information in respect of at least one relevant piece of information (Daughety and Reinganum 2012, p. 394). This needs to be distinguished from two-sided asymmetric information, where both parties have private information in respect of a relevant aspect (Daughety and Reinganum 2014, 86 Fn.6). If the relevant piece of information concerns one of the players, i.e., their payoff, valuation, or their costs of performance it is called a game of incomplete information (Mas-Colell et al. 1995, p. 253). We transform the game of incomplete information to a game of imperfect information by adding a so-called first move by nature choosing the realization of the parties’ respective attributes like his valuation or costs of performance with a certain probability distribution. This approach originates from John Harsanyi. See for more details Mas-Colell et al. (1995, p. 254).

Note that observable does not imply that the piece of information is verifiable (Schwartz and Scott 2003, 605). For a party to verify a piece of information it is a necessary condition that the piece of information is observable to that party. In addition, the party needs to be able to demonstrate the piece of information. This ability is not only limited by the mere power to do so but also by the costs it entails. Verifying the piece of information can be of interest regarding both the opposite party or a third party, in particular a court (Schwartz and Scott 2003, 605).

Ben-Shahar and Bernstein (2000); this statement holds as long as all buyers would sue upon breach of contract: see Avraham and Liu (2012) for an analysis if not all buyers would sue. In their model new information about the buyer’s valuation and the seller’s costs arises after the conclusion of the contract. The information is two sided-asymmetric. They find that the court should not include the new information about the valuation into its assessment of damages; in particular if the parties can renegotiate.

It has been argued that the importance of incomplete information is less relevant under expectation damages because compensation could be calculated on the basis of the difference between the contract price and the market price, see Schwartz (1979, 285). But, the difference between the contract price and the market price is unlikely to make the buyer indifferent. If there is a market price the buyer is likely to have paid the market price. Even if the buyer paid less than the market price his valuation is nevertheless likely to exceed the market price. Most notably, as outlined above, the efficient breach scenario and the discussion about remedies claims the more importance the less the good subject to the contract is fungible or homogenous. It follows that in the most relevant cases there would be no market that could function as the benchmark to come up with some market price.

On a general basis it is true that the problem of incomplete information is alleviated if a market exists. Consider a seller and a buyer operating in a market with homogenous goods. The seller and buyer concluded a contract based on the market price. In case the seller’s costs of performance increase above the market price she does not necessarily know whether her costs have increased above the buyer’s valuation, but she can infer that covering is the cheapest option because the buyer’s valuation will be above the market price.

Eisenberg calls it “efficient termination.”

See for a richer model on bargaining under property and liability rules with one-sided asymmetric information (Engert and Hofmann 2019). Their model contains a continuous type space for the owner of an entitlement (buyer).

Ausubel, Cramton and Deneckere refer to the former kind as the “gap cases” and call the latter ones “no gap cases,” see Ausubel et al. (2002).

See for an exception: Spier (1992).

A model that allows an infinite time horizon and also for alternating offers is the Rubinstein bargaining model. To keep it simple I concentrate on one round of offers.

This would be different if the buyer’s valuation turns out to be lower than the price after the seller has breached. See for an analysis focusing on the effect that buyers do not sue Avraham and Liu (2009). In their model new information about the buyer’s valuation and the seller’s costs arises after the conclusion of the contract. The information is two sided-asymmetric. They find that the court should not include the new information about the valuation into its assessment of damages; in particular if the parties can renegotiate. In addition, they find that if low valuing buyers do not sue under specific performance it can foster efficiency.

This is a common assumption, see Daughety and Reinganum (2012, p. 391).

This is a common assumption, see Daughety and Reinganum (2012, pp. 386, 388).

As said before, in such situation it is plausible to assume that the buyer accepts the offer equal to his valuation and is therefore indifferent. The seller could increase the offer by an incremental amount and the buyer prefers to accept. The incremental amount tends towards zero because the smaller it is the greater the seller’s payoff.

See Footnote 13.

Kaplow and Shavell (1996b, 737 Fn. 711). They refer to Johnston (1995) and Spier (1992) for earlier versions of that argument.

See for a model on bargaining under property and liability rules with one-sided asymmetric information with a continuous type space Engert and Hofmann (2019).

Making offers between v _α − P and v _β − P is not in equilibrium because β types would still not agree and the seller makes a higher payments to type α.

For example, in a case concerning lost earnings, the German Federal Court decided that to determine damages one can assume that the plaintiff would have earned at least an amount he would have received with average success in his job; BGH 6.2.2001.

Importantly, we assume that the court would still decree average damages and not swop to award damages based on the low type’s valuation.

A situation similar to a shortfall of damages but concerning both kind of remedies arises if the contractual entitlement itself is uncertain to be granted. Johnston (1995) finds that such uncertainty has a positive effect on the efficiency of bargaining with asymmetric information. Croson and Johnston (2000) find positive evidence for the predictions in an experiment.

This relationship was already discussed in Chap. 3 with the focus on distributional effects and complete information.

See for the argument in the context of defective toasters: Craswell (2003, 1158, 1159).

Rothschild and Stiglitz addressed this problem in their seminal article: Rothschild and Stiglitz (1976).

In subsequent sections the analysis will depart from the assumption that the parties reach efficient agreements ex post and assess how that affects the contracting stage.

This is also the result of Chap. 3.

In the analysis above we had three buyers with one of them having a valuation above the seller’s increased costs. With regard to the two buyers with valuations below the seller’s costs the result carry over. Our assumption that an efficient ex post outcome is achieved precludes the outcome that the seller offers a side payment equal to the low type’s valuation which is only accepted by the low types.

If the seller made an offer equal to the low type’s valuation the high type would not accept leading to an ex post efficiency.

Besides verification costs to be zero it is an important assumption that the buyer knows his type and the seller being aware of that. See for more details and to what the given conditions do not only sufficient but also necessary conditions: Bolton and Dewatripont (2015, pp. 176, 178).

See also for the full unraveling effect under expectation damages: Bebchuk and Shavell (1991, 284), Faust (1996, p. 231).

The full disclosure theorem was established by Grossman and Hart (1980), Grossman and Leland (1981), Milgrom (1981).

Another potential limit to disclosure is law prohibiting price discrimination. However, this seems little relevant for the topic of the efficient breach scenario and a company on both sides of the contract. For instance, this is more important regarding insurance contracts and anti-discrimination law; see ECJ 1. March 2011.

The following outlines the detailed deduction. First consider the seller to make the take-it-or-leave-it offer.

The buyers’ payoff which constitutes the participation constraints allow us the derive the prices the seller offers:

The seller’s payoff function depends on the type of buyer she faces.

We derive the seller’s payoff facing a low type

The seller’s payoff facing a high type is

In both cases the seller captures all gains from trade. The seller’s payoff also representing the total payoff is

Next, consider the buyer to make the take-it-or-leave-it offer:

Thus, the price the low type offer is \( P=\left(1-\alpha \right){c}^o+\alpha \underset{\_}{v} \).

The high type offers a price P = (1 − α)c ^o + αc.

This provides the following payoffs to the buyer:

This provides us with the following total payoff

If one supposes that under specific performance the seller makes a side payment to the buyer equal to her increased costs, we would not observe cross-subsidization in the first place as shown above.

Similarly Ayres and Gertner as well as Bebchuk and Shavell make the distinction whether it is desirable that the seller can distinguish between buyers with a high or a low valuation to take the efficient decision, see Ayres and Gertner (1989, 101), Bebchuk and Shavell (1999, 1617).

Recall that the assumption is that the parties do not reach an efficient outcome ex post.

9 Ex. 341, 156 Eng. Rep. 145 (1854). Classic nineteenth century English case where a mill owner, Hadley, engaged the company Pickford & Co. to deliver an engine shaft to another city for replacement. Pickford and Co. belonged to Baxendale (the defendant). The performance of that contract was of high value to Hadley because he did not have a spare shaft and without a new shaft his mill could not operate. Baxendale did not deliver the shaft on the agreed date and Hadley incurred damages because he could not operate his mill. The court ruled that Baxendale did not have to compensate Hadley for his loss because Baxendale could not foresee them. Hadley would have had to have communicate the particular circumstances to Baxendale at the time the contract was concluded.

Bebchuk and Shavell compare limited (no damages for unforeseeable losses) and unlimited liability for damages. In their model the seller can take precautions in order to be able to perform. In their model two types of buyers exist: Few high valuing buyers and many low valuing buyers. The seller cannot observe the buyer’s valuation. Bebchuk and Shavell assume that the buyers can identify themselves either as high or low valuing buyers. If a buyer reveals his type, he incurs communication costs. Adler extended this model by adding that high types do not only suffer higher damages but also that they are more likely to suffer damages [See Adler (1999) and the response by Bebchuk and Shavell (1999)]. However, in the context of the efficient breach scenario it seems not convincing that a buyer who does not receive performance would not suffer damages regardless of his valuation.

See also Bigoni et al. (2017, 28), who state that the option to breach would lead to an exchange of information in the scenario that the buyer has superior information about the seller’s costs of performance or the converse setting that the seller has superior information about the buyer’s valuation if damages are undercompensatory. But they do not provide a closer assessment. In particular they do not discuss to what extent damages need to be undercompensatory in relation to the profit the informed makes on having superior information.

Johnston (1990, 631) arrives at the same conclusion for the standard case of the foreseeability doctrine assuming a fixed standard of precaution. In such case more information about the buyer’s valuation does not lead to more efficient precautions.

Bebchuck and Shavell (1991) reach the analogous result for the scenario that the seller exercises a certain level of precaution instead of willful breach in a perfectly competitive market.

See for a simple model which shows price discrimination by the seller if she learns about the buyer’s valuation but neglecting the effects of remedies: Ben-Shahar and Bernstein (2000, 1890 Fn. 13).

See for an overview of this discussion: Faust (1996, pp. 318–320).

In case the high type did not inform the seller about his type because he prefers to keep that information secret this would not change after the conclusion of the contract with respect to future contracts and third parties.

Cross-subsidization is not such a problem if the all buyers learn their true valuation only after the conclusion of the contract. Low buyers still subsidize high types. But because the buyer does not know what type he is when he concludes the contract this would not cause buyers deciding not to contract at all. To have a law differentiating between the case that the buyer only learned his valuation after the conclusion of the contract seems impractical due to problems how to proof not having this knowledge prior to a certain point in time.

The thought has been expressed by Ayres and Gertner (1989, 102 Fn. 66) with regards to the situation that the seller takes a certain level of precautions and without analyzing it in more detail; Johnston (1990, 636) further developed this point.

We would arrive at the same conclusions if we suppose that the seller performs under unlimited liability.

This could either be because the foreseeability doctrine is interpreted in the sense that paying a high price signals to be a high type. Alternatively, the seller could include such clause in the contract with the high price.

I focus on the interesting case that the seller prefers to contract with both types and not only the high type.

So-called participation constraints which we have encountered before.

So-called incentive constraints.

See Johnston (1990, 628) for an analysis if the seller can charge only a single price.

An alleged disadvantage of the foreseeability doctrine is the information costs created due to its ambiguity which we will not further discuss in this context: Bebchuk and Shavell (1991, 284, 308), Faust (1996, p. 237).

As said above, additionally the high type might put a value on not disclosing his valuation in the light of future contracts. See also for this point Ben-Shahar and Bernstein (2000).

See for such argument: Ben-Shahar and Bernstein (2000, 1893).

The related underlying question is: Why should the buyer’s interest to keep his valuation private be protected; and if yes of which type of buyer? Shahar and Bernstein argue that from a social welfare perspective, taking the buyer’s interest to keep information private into account bases on the incentive it creates to acquire information or invest in innovation (Ben-Shahar and Bernstein 2000, 1893 Fn. 21). In the given context, the argument would be that the high type was more innovative and therefore has a greater valuation. If he could not fully profit from having the greater valuation he would not be incentivized efficiently to invest in innovation. However, it is far from clear that the high type’s greater valuation stems from innovation. It could simply be that the high type is less prepared for a certain situation and therefore needs the specific good more urgently leading to greater valuation in that moment. Putting it generally, whether the buyer’s private information about his valuation should be protected is a complex question which depends on context and cannot be answered on a general basis. See for an law and economics approach to the question what kind of information should be protected: Hirshleifer (1971).

This result differs from the assertion by Ben-Shahar and Bernstein that specific performance would preserve the buyer’s secrecy interest; see Ben-Shahar and Bernstein (2000, 1904). In addition, at the renegotiation stage the seller would learn the buyer’s type if renegotiation is successful.

A similar point is made by Ayres and Gertner (1989, 110–111).

Those assumptions have been critically viewed by Johnston (1990, 623).

This result potentially differs once we depart from rational choice in the light that research has shown that default rules are “sticky.”

This point has originally been made by Shavell (1980, 468 Fn. 6) without further inspection: “… the seller might wish to renegotiate owing to an increase in production costs, and let us assume that the increase is such that the total costs are still below the value of the machine to the buyer. If the buyer does not know what the production costs really are and he thinks the seller is bluffing he might refuse to accommodate the seller, (…).”

Importantly, this analysis bases on the assumption that the seller cannot verify her costs. Otherwise, under the conditions outlined in Sect. 6.1.3.2, we would find the high type seller to reveal her type.