Market Structure

Abstract

We reject the market structure hypothesis, as theorized by Kessler (1943), who argued that the risk of unfair clauses is very high especially in those markets in which sellers have market power, above all in the case of a monopoly. By contrast, we prove that unfair clauses are ubiquitous across market structures.

Appendix

We now use the game-theoretical model presented in the Appendix of the previous chapter, and solve the game searching for (symmetric) equilibria in both a monopoly and a competitive market.

As already highlighted in the chapter, we assume that consumers are all sophisticated: this assumption will be relaxed in the next chapter.

As a benchmark case, we first prove that the equilibrium would be efficient in both markets if consumers were able to read fine print at no cost (viz. k = 0).

Result 2.1 (Free reading)

If k = 0 then in equilibrium both a monopolist and competitive sellers offer friendly clauses and charge, respectively, u _h and c. Consumers accept and get 0 if they face a monopolist, whereas they get all the market surplus if they face a competitive seller. These equilibria are efficient.

Intuition

Not reading is weakly dominated because k = 0. Consumers’ reservation prices for a friendly and an unfriendly contract are, respectively, u _h and u _l (where u _h  > u _l ) so that neither an unfriendly contract charging more than u _l nor a friendly contract charging more than u _h can be offered in equilibrium since consumers would reject.

A monopolist earns at most u _l from an unfriendly contract and u _h  − c from a friendly contract. The Efficiency Condition implies that u _h  − c > u _l , so a monopolist has always an interest to offer a friendly contract. Consumers accept and earn 0.

Competitive sellers cannot offer an unfriendly contract at any price p < u _l since another seller could attract all consumers by offering a friendly contract and charging a price p′ such that u _h  − p′ > u _l  − p and this price always exists because p < u _l  < u _h .

In turn, sellers must offer a friendly contract and competition will force them to charge the lowest possible price p = c. Consumers accept and earn u _h − c, whereas sellers earn 0.

Let now assume that the reading cost is strictly positive (viz. k > 0).

Result 2.2 (Monopoly)

a. A monopolist offers an unfriendly contract charging p = u _l and consumers accept earning 0 in the only pure strategy equilibrium. Both parties get positive payoffs. This equilibrium is inefficient;

b. If the reading cost is small enough and u _h is large enough, a monopolist mixes between friendly and unfriendly clauses charging  $p \in (c, u_{h}-k)$ ; consumers mix between reading and accepting without reading. Every player gets positive expected payoffs. This equilibrium is inefficient.

Intuition

a. Belief consistency excludes an equilibrium in which a monopolist offers a friendly contract charging any $p \le u_{h}$: for consumers would always buy without reading and, since they would not read, the monopolist would profitably deviate to an unfriendly contract charging the same price in order to economize on the production cost c.

Conversely, there is an equilibrium in which the monopolist offers an unfriendly contract charging u _l . Since consumers accept [resp. reject] without reading at any price $p \le u_{h}$ [resp. p > u _l ], no deviation to any other unfriendly contract is profitable for the monopolist. He cannot deviate to a friendly contract if consumers believe that it is rather unfriendly (see adverse inference, Sect. 1.7).

This equilibrium is inefficient because sellers offer unfriendly contracts (see the Efficiency Condition, Appendix of Chap. 1);

b. Consumers are indifferent between reading and accepting without reading only if they get the same payoff from both strategies. This is feasible only if the monopolist does not offer friendly or unfriendly clauses for sure, but mixes between the two alternatives. Call γ the consumers’ belief that a contract is friendly. In order to mix, the monopolist must get the same payoff from both contracts: it implies that p > c, otherwise the monopolist will never offer a friendly contract; and $p < u_{h}-k$, otherwise consumers would not read as they would get less than 0 because γ < 1. Consumers get γu _h  + (1 − γ)u _l  − p if they accept without reading and γ(u _h  − p) − k if they read, so that they are indifferent only if

$$ p = u_{l} + \frac{k}{1 - \gamma } $$

(2.1)

They do not deviate to not buying without reading only if they get positive payoffs in equilibrium, that is, γu _h  + (1 − γ)u _l  − p > 0. Substituting for p, this condition that is satisfied for some values of γ ∈ (0, 1),¹⁰ precisely:

$$ \gamma \in \left( {\frac{1 - Y}{2},\frac{1 + Y}{2}} \right), $$

(2.2)

where

$$ Y = \sqrt {1 - \frac{4k}{{u_{h} - u_{l} }}} \qquad{\text{requires}}\;k \le \frac{{u_{h} - u_{l} }}{4}. $$

A monopolist earns p − c if he offers friendly clauses and (1 − r)p if he offers unfriendly clauses, where r is the probability that consumers read. Therefore, to be indifferent it must be

$$ \begin{aligned} & p - c = (1 - r)p \\ & \Rightarrow r = \frac{c}{p} \\ \end{aligned} $$

where p > c in order to assure that the monopolist gets a positive payoff. A monopolist does not deviate to an unfriendly contract charging exactly u _l if p − c > u _l , which requires $\gamma > 1 - k /c$. This last condition is satisfied at least for the highest value of γ in condition (2.2) if either k > c or k < c and

$$ u_{h} > u_{l} + \frac{c^2}{c-k} $$

Adverse inference (see again Sect. 1.7) excludes any other deviation to a friendly contract charging any out-of-equilibrium price.

This equilibrium is socially inefficient because the monopolist offers unfriendly clauses only with some positive probability and consumers pay the reading cost with some positive probability (see again the Efficiency Condition, Appendix of Chap.1).

Result 2.3 (Competition)

a. Competitive sellers offer an unfriendly contract charging 0 and consumers accept earning u _l in the only pure strategy equilibrium. This equilibrium is inefficient;

b. If the reading cost is small enough and u _l > c, sellers mix between friendly and unfriendly contracts charging $p \in (c, u_{h}-k)$; and consumers mix between reading and accepting without reading. Both sellers and consumers get positive payoffs. This equilibrium is inefficient.

Intuition

a. Suppose that all sellers offer an unfriendly contract charging 0 and consumers accept. Sellers earn 0 and consumers earn u _l . Sellers cannot deviate to charging a price greater than 0 since other sellers would make all sales. No seller can profitably deviate to a friendly contract: for they should charge more than c in order to get positive payoffs, but consumers would not buy if they adversely infer that the deviating contract is unfriendly (see adverse inference, Sect. 1.7).

This equilibrium is inefficient because sellers offer unfriendly contracts (see the Efficiency Condition, Appendix of Chap. 1);

b. Again, as shown for the monopoly (see Result 2.2b above), sellers can mix between reading and accepting without reading only if consumers mix between reading and accepting without reading, and vice versa: precisely, sellers and consumers must get the same payoff from both their own strategies. Therefore, conditions (2.1) and (2.2) as found in the previous Result at part b apply for the competitive market as well, where p > c assures that sellers get positive payoffs, and always holds if u _l > c; whereas $p < u_{h}-k$ assures that consumers read with positive probability.

No seller has an interest to charge a price lower than the equilibrium range because consumers would infer that such contract includes unfriendly clauses, and would reject. Similarly, no seller has an interest to deviate to a friendly contract charging more than the equilibrium range of price because consumers do not expect such offer in equilibrium and would not trust the seller.

We now exclude a deviation to an unfriendly contract. To gain from such deviation, the deviating seller should be able to attract all consumers. It requires that the deviating contract must include a price q such that

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

where the left-hand side on the first row is consumers’ expected utility in the mixed strategy equilibrium, and the right-hand side is consumers’ utility from switching to the deviating seller. That seller would therefore get strictly less than q, which turns out unprofitable if

$$ q < \frac{p - c}{N} $$

(2.3)

Since p > c, condition (2.3) is satisfied if q < 0, which requires

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

(2.4)

where

$$Z=\sqrt{\frac{(u_{h}-2u_{l})^{2}-4k(u_{h}-u_{l})}{2(u_{h}-u_{l})}}\,requires\,k<\frac{(u_{h}-2u_{l})^{2}}{4(u_{h}-u_{l})}$$

It is easy to show that

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

so that condition (2.4) proves the claim. This equilibrium is socially inefficient because the monopolist offers unfriendly clauses with some positive probability and consumers pay the reading cost with some positive probability (see the Efficiency Condition, Appendix of Chap. 1).