Voluntary Disclosure of Clauses

Abstract

We now allow sellers to disclose their hidden clauses at some positive cost. We show that, contrary to conventional wisdom, if naïve consumers are few enough a monopolist is more likely to disclose (and therefore to offer efficient friendly clauses) than competitive sellers. By contrast, if enough consumers are naïve, then disclosure takes place only in a competitive market.

Appendix

Suppose that sellers can decide to disclose their contracts at some cost δ > 0.

To make disclosure attractive on a social point of view, we will assume that δ ≤ k: it means that disclosing the contract for a seller is cheaper than reading the contract for consumers.

We distinguish two cases. First, we assume that all consumers are sophisticated; then, we introduce a fraction θ > 0 of naïve consumers.

4.1.1 Sophisticated Consumers

We start from some general results that always hold irrespective of the market structure.

Result 4.1

a. A disclosing seller must offer friendly terms.

b. No seller can offer a friendly contract with some positive probability in equilibrium without offering an unfriendly contract at the same price, unless he discloses.

Intuition

Proof is given by contradiction.

a. Suppose that a disclosing seller offers unfriendly terms. Consumers freely read unfriendly clauses and reject the contract if charged more than u _l . That seller then gets no more than u _l  − δ and can profitably deviate to not disclosing at the same price to economize on the disclosing cost.

b. Part b. excludes (i) equilibria in pure strategies with a seller offering a non-transparent friendly contract; (ii) equilibria in mixed strategies where a seller does not disclose and mixes between friendly and unfriendly terms charging different prices, and (iii) equilibria in mixed strategies in which a seller offers friendly clauses and mixes between disclosing and not disclosing.

About (i), suppose that a seller does not disclose and offers a friendly contract charging p > c without offering an unfriendly contract: consumers always accept without reading at any $p \le u_{h}$ because they attach a probability equal to 1 that the equilibrium contract includes friendly terms, and the seller would profitably deviate to offering an unfriendly contract at the same price to economize on c.

A similar reasoning applies to (ii) if a seller does not disclose and mixes between a friendly contract charging p and an unfriendly contract charging $q \ne p$. For the seller being indifferent it must be $p = q + c$. Consumers could infer the contract quality looking at the price and would always accept without reading if $p \le u_{h}$ and $q \le u_{l}$ However, the seller could profitably deviate to an unfriendly contract charging p to economize on the production cost.

About (iii), the previous reasoning in (ii) also excludes an equilibrium in which a seller discloses with some positive probability. Suppose now that a seller offers a friendly contract and mixes between disclosing charging p and not disclosing charging q. To be indifferent it must be $p = q + \delta$. Consumers would accept any offer without reading for every price $p \le u_{h}$, and the seller would profitably deviate to a non-transparent unfriendly contract charging q to economize on the production cost c.

In sum, a non-disclosing seller must mix between a friendly and an unfriendly contract charging the same price p. It is impossible if consumers always read or accept without reading because the seller would never offer respectively un unfriendly or a friendly contract. Then, consumers must mix between reading and accepting without reading.

Result 4.2 (Monopoly)

A monopolist always discloses and offers friendly clauses charging $p = u_{h}$ . Consumers accept and earn 0. This equilibrium is unique and efficient. A monopolist always gains from disclosure, whereas consumers can only lose.

Intuition

A disclosing monopolist must offer friendly clauses (see Result 4.1): he has no interest to charge less than u _h because consumers would buy at that price and the monopolist would simply reduce his profits. The monopolist gets $u_{h} - c - \delta$. Suppose he deviates to a non-transparent contract. He cannot charge more than u _l if consumers infer that the deviating contract contains unfriendly terms. Such a deviation turns out unprofitable according to the Efficiency Condition because $\delta \le k$.³ It also proves that this equilibrium is efficient because friendly clauses are offered in equilibrium.

We now prove that this equilibrium is unique.

Result 4.1b excludes any other equilibrium in pure strategies or in mixed strategies unless the monopolist charges p > c and mixes between friendly and unfriendly clauses, and consumers mix between reading and accepting without reading. The monopolist must charge less than u _h  − k in such a putative equilibrium, otherwise no consumer would read with positive probability in equilibrium. He would then get strictly less than u _h  − c − k, and could profitably deviate to disclosing because $\delta \le k$. A similar reasoning excludes an equilibrium in which the monopolist discloses with some positive probability.

Note that a monopolist gets u _h  − c − δ, and always gains from disclosure because $\delta \le k$; whereas consumers get 0 and can only lose from disclosure as they would have got positive payoffs in some equilibria (see Result 2.2b for a comparison).

Result 4.3 (Competition)

a. Sellers offer a transparent contract charging $p=c+\delta$ , and consumers accept. This equilibrium is efficient. No other equilibrium exists if the reading cost is large enough; otherwise,

b. If the reading cost is small enough, sellers do not disclose and mix in equilibrium between friendly and unfriendly, both priced at some $p\in(c,u_{h}-k)$ ; consumers mix between reading and accepting without reading. This equilibrium is inefficient.

Sellers are unaffected by disclosure, whereas consumers gain from matching a disclosing seller.

Intuition

a. Proof follows the same line of that given for Result 4.2a. The only difference is in the equilibrium price that is lower than in a monopoly, and equal to sellers’ costs. No seller can charge a higher price in equilibrium because the contract is transparent, so that consumer can compare the offers and always buy from sellers charging the lowest price. This equilibrium is efficient because sellers offer friendly clauses (see the Efficiency Condition).

b. Result 4.1b again implies that the only case to analyze is that with sellers mix between not disclosing and mixing between friendly and unfriendly clauses, and consumers mixing between reading and accepting without reading. Proof follows a similar line of that given for Result 2.3b, so that conditions (2.1) and (2.2) still apply with u _l > cl and $p\in(c,u_{h}-k)$ (see the Appendix of Chap. 2). We have just to exclude that deviating to either an unfriendly contract or to disclosing is profitable for sellers. In order to attract consumers, a disclosing seller should offer friendly clauses (see Result 4.1) charging a relatively cheap price q such that consumers prefer buying from him. It requires

$$\begin{aligned} & \gamma u_{h} + (1 - \gamma )u_{l} - p < u_{h} - q \\ & \Leftrightarrow q < (1-\gamma)(u_{h} - u_{l} ) + p \\ \end{aligned}$$

where the left-hand side of the first inequality is consumers’ utility from a non-transparent contract and the right-hand side is consumers’ utility from switching to a disclosing seller who charges q. The deviating seller would therefore get strictly less than q − c − δ. The efficiency Condition implies that $(1-\gamma)(u_{h}-u_{l})+p-c-\delta > p-\gamma(u_{h}-u_{l})$ because δ ≤ k where the right-hand side is a seller's payoff from deviating to an obscure unfriendly contract (see result 2.3b). Therefore, a sufficient condition to exclude every possible deviation becomes

$$q - c - \delta < 0$$

which requires

$$\gamma\in\left(\frac{2u_{h}-u_{l}-c-\delta-A}{2(u_{h}-u_{l})},\frac{2u_{h}-u_{l}-c-\delta+A}{2(u_{h}-u_{l})}\right),$$

where

$$A=\sqrt{(c+\delta-u_{l})^{2}-4k(u_{h}-u_{l})} \ is \ well \ defined \ if \ k\leq\frac{(c+\delta-u_{l})^{2}}{4(u_{h}-u_{l})}$$

If u _l < c + δ, it is easy to show that 

$$\left(\frac{2u_{h}-u_{l}-c-\delta-A}{2(u_{h}-u_{l})},\frac{2u_{h}-u_{l}-c-\delta+A}{2(u_{h}-u_{l})}\right) \subset\left(\frac{1-Y}{2},\frac{1+Y}{2}\right),$$

proving the claim.

Note that sellers cannot gain from disclosure because they cannot charge more than their costs. At the same time, they do not lose because they still do not disclose and get positive payoffs in the equilibrium above in which they mix. By contrast, consumers gain from matching a disclosing seller as they get u _h - c - δ, whereas they would have got strictly less without disclosure (see Result 2.3 for a comparison).

4.1.2 Naïve Consumers

Let now assume that a proportion θ > 0 of consumers is naïve, as well as we did in the previous chapter. We assume that naïve consumers become sophisticated, and therefore fully informed, only if they match a disclosing seller, except a proportion $\omega \le \theta$ that always remains unaware. Accordingly, naïve consumers remain naïve (viz. ω = θ) if they match a non-disclosing seller. The last point implies that if competitive sellers charge different prices because only some of them disclose, then naïve consumers always buy from those charging the lowest price regardless of whether these sellers have disclosed or not.

Result 4.4 (Monopoly)

A monopolist always charges u _h . He discloses and offers friendly clauses if and only if θ is small enough. If $\theta$ is large enough, then a monopolist does not disclose and offers unfriendly clauses. A monopolist always gains from disclosure, whereas consumers can only lose.

Intuition

A monopolist could charge u _h for a fully transparent contract and would earn u _h  − c − δ if he offers friendly clauses or ω(u _h  − δ) if he offers unfriendly clauses. If he deviates to a non-transparent contract, then he has to charge no more than u _l to sell to all consumers, whereas he would sell to naïve consumers only if he charges a higher price. In either case, the monopolist would include unfriendly clauses getting either $u_{l}$ or $\theta u_{h}>\omega(u_{h}-\delta)$. None of these deviation is profitable if θ is small enough and u _h  − c − δ > u _l . The last condition always holds in equilibrium because δ≤k (see the Efficiency Condition in the Appendix of Chap. 1). Note that the monopolist never mixes between friendly and unfriendly contracts at the same price without disclosing for the same reasons presented in Result 4.2.

A monopolist gets u _h  − c − δ, and always gains from disclosure because δ ≤ k.

Consumers earn 0 if the monopolist discloses, so they cannot gain and sometimes lose in respect to those mixed-strategy equilibria in which they would have got a positive payoff (see Result 3.1 for a comparison).

Result 4.5 (Competition)

a. Sophisticated consumers trade with competitive sellers who disclose and offer a friendly contract charging c + δ, and naïve consumers trade with sellers who do not disclose and offer an unfriendly contract charging 0.

b. If θ is small enough, there exists a mixed strategy equilibrium as such characterizing the game with sophisticated consumers only, in which naïve consumers always accept without reading.

Sophisticated consumers alone gain from matching a disclosing seller.

Intuition

a. The specified strategies form an equilibrium if sophisticated consumers believe that a deviating seller who does not disclose offers unfriendly clauses (see adverse inference, Sect. 1.7). Sophisticated consumers trade with disclosing sellers charging c + δ and do not deviate to those charging 0 because u _h  − c − δ > u _l . Again, it comes straightforward from the Efficiency Condition because δ ≤ k. Naïve consumers are attracted by sellers who charge the lowest price and get u _l .

All sellers earn 0 and none of them can profitably deviate to charging higher price for either a transparent or non-transparent contract because they would not trade. By contrast, no equilibrium can exist in which all sellers disclose and charge c + δ because they could get a positive payoff by deviating to a non-disclosed unfriendly contract charging a slightly lower price to attract naÏve consumers.

b. If naÏve consumers are few enough they are not able to influence the equilibrium outcome that remains unchanged and follows the same line of that presented in Result 4.3b. with sophisticated consumers only.

Conversely, mixed strategy equilibria cannot survive if naïve consumers are numerous enough because each seller could profitably deviate to an unfriendly obscure contract charging a slightly smaller price to attract naÏve consumers.

Note that sellers cannot gain from disclosure as they have to charge a price equal to their costs. At the same time, they do not lose because they do not disclose and get positive payoffs in some equilibria if both k and θ are small enough. Sophisticated consumers get u _h  − c − δ and always gain from matching a disclosing seller as they would have got strictly less without disclosure. Naïve consumers never match a disclosing seller, so that they do not gain and do not lose from disclosure (see Result 3.2 for a comparison).