Intermediation in a Sharing Economy: Insurance, Moral Hazard, and Rent Extraction

Abstract

A key impediment to sharing is a lender’s concern about damage to a lent item due to unobservable actions by a renter, usually resulting in moral hazard. This paper shows how an intermediary can eliminate the moral hazard problem by providing optimal insurance to the lender and first-best incentives to the renter to exert care, as long as market participants are risk neutral. The solution is illustrated for the collaborative housing market but applies in principle to any sharing market with vertically differentiated goods. A population of renters, heterogeneous both in their preferences for housing quality and with respect to the amount of care they exert in a rental situation, face a choice between collaborative housing and staying at a local hotel. The private hosts choose their prices strategically, and the intermediary sets commission rates on both sides of the market as well as insurance terms for the rental agreement. The latter are set to eliminate moral hazard. The intermediary is able to extract the gains the hosts would earn if transacting directly. Finally, even if hotels set their prices at the outset so as to maximize collusive profits, collaborative housing persists at substantial market shares, regardless of the difference between the efficiencies of hosts and hotels to reduce renters’ cost of effort. The aggregate of hosts, intermediary, and hotels benefits from (a variety in) these effort costs, which indicates that the intermediated sharing of goods is an economically viable, robust phenomenon.

Key words and phrases:

• collaborative consumption
• digital economy
• incentive contracting
• intermediation
• moral hazard
• optimal insurance
• sharing economy
• trust

Acknowledgments

The author thanks Heski Bar-Isaac, Eric Clemons, Ali Hortaçsu, Robert Kauffman, Roman Rochel, Larry Samuelson, participants in the 2014 Hawaii International Conference on System Sciences (HICSS), and several anonymous referees for helpful comments and suggestions.

Appendix A: Proofs

Proof of Theorem 1. The five subsets for p₀ indicated in Table 1 are examined in turn. For clarity, we restrict attention to the interior of each subset. Showing the continuity of the solutions by checking the one-sided limits at the boundaries of each segment is elementary and therefore omitted.

Table B1. Summary of notation

a. If then the hosts’ respective profits are and , where is the consumer type indifferent between the two hosts. The hosts’ best-response functions are

Intersecting the hosts’ best responses yields the unique Nash equilibrium prices

At these prices, the type indifferent between the two hosts is . Furthermore, the demand for the outside option vanishes because

b. If , then the hosts’ profit-maximizing prices are

At these prices, the indifferent types , , are such that

Consequently, the hosts’ (positive) equilibrium demands are and , respectively.

c. If , then host 1 offering the low-quality accommodation cannot break even. His market share therefore vanishes (). By offering a superior-quality accommodation, host 2 manages to stay in the market. The expressions for his optimal price and his equilibrium demand correspond to those given under b.

d. If , then collaborative housing is not viable (). The outside option is so cheap that it effectively undercuts any price at which the hosts would obtain a positive gain.

e. If , then at the Nash-equilibrium prices determined under a. the demand for hotels would become positive. On the other hand, the presence of the outside option effectively decouples the competition among the hosts, whose respective demands are and Since , it is necessarily . Hence,

for , corresponding to . As a result,

Because of the linearity of the model, the slope of and is constant in . Using the results obtained under a. and b., continuity at the interval boundaries implies that²⁴

and

The boundary conditions for , for yield

and consequently,

for all

By continuity, a. through e. together establish the results for the prices and the demands in Table 1 for all . The hosts’ respective profits are obtained from these results by computing

Proof of Corollary 1. The comparative statics for host 1 obtain via direct differentiation of the results in Table 1 with respect to the excess price . For host 2, the comparative statics obtain directly for the price . For , it is if and only if which on that segment is always satisfied. For all other segments, is trivially non-decreasing in . Lastly, host 2’s demand is first non-decreasing (for ) and then non-increasing (for ), which follows directly via differentiation of the corresponding expression in Table 1 with respect to . QED

Proof of Corollary 2. From Theorem 1 if follows that if and only if , and if and only if . QED

Proof of Lemma 1. (i) Consider first the case where are fixed with are fixed, and let be in the interval . Then

and, using the Leibniz rule,

This derivative vanishes if , which is a maximizer (yielding ), since is strictly concave in (i.e., ); this can be seen by differentiating the last expression using again the Leibniz rule. In the case where , the renter’s liability is maximized for , and

(ii) For , the renter’s liability is by part (i) equal to , and therefore increasing in .

Thus, the smallest deposit for which must be . QED

Proof of Lemma 2. Since the renters’ cost types are heterogeneous, at an expected liability of (by R1) it is not guaranteed that the probability of damage vanishes. Hence, R3 can in general only be satisfied if the expected capital-at-risk vanishes,

The host’s expected agency cost consists of his expected contribution conditional on damage times the probability of damage. As discussed earlier, does not generally vanish. Hence, to ensure that R2 () is always satisfied, necessarily

Hence R2 and R3 lead to the same restriction, namely that . QED

Proof of Theorem 2. Combining the conditions in Lemma 1 and Lemma 2 for satisfying the requirements R1–R3 leads to the conditions in Theorem 2. QED

Proof of Lemma 3. Let the intermediary’s cost for enabling the housing transactions be . Given the commission structure , the intermediary obtains the fraction h from the host’s revenue and (roughly speaking) the fraction of the renter’s payment at nominal prices, resulting in the profit

Since and host ’s profit can be written in the form

one obtains

which completes the proof. QED

Proof of Lemma 4. By R2, it is. Hence, the effective agency cost is and thus independent of . Table 1 then implies all of the conclusions. QED

Proof of Lemma 5. This result follows from Table 1 when setting . QED

Proof of Lemma 6. The assertions follow directly from Theorem 1 and Lemma 4. QED

Proof of Lemma 7. Given that the intermediary’s insurance terms satisfy requirement R2, transacting directly increases the effective agency costs by

Thus, on the one hand one obtains a lower bound,

and on the other hand,

which yields an upper bound. The lower bound is achieved if the cost-type distribution has all its mass at . The upper bound becomes arbitrarily close to binding when the cost-type distribution has equal point mass (of ) at the two points and , respectively, and . QED

Proof of Theorem 3. As noted in Lemma 6, the intermediary’s profit is increasing in when the hosts do not have any outside options to earn economic rents from (sub-)letting their private space. Let be fixed. By Theorem 1 (and Table 1) host ’s equilibrium profit is such that

for all admissible . For both hosts’ direct-transaction profits to be smaller than under an intermediated transaction, the commission ratio needs to stay finite. More specifically,

so that

for . The formula for the optimal commission ratio in in the statement of the proposition takes the smaller of the two constraints (for ) as binding.²⁵ The symmetric commission rates follow immediately from the relation . QED

Proof of Corollary 4. The matching-enhanced optimal commission ratio obtains from the individual-rationality conditions

for both hosts . Note that for these conditions specialize to what was discussed at the beginning of the proof of Theorem 3. QED

Proof of Theorem 4. The demand for hotels (as a function of ), is where and are given in Theorem 1. In order for demand to remain positive, Table 1 implies that the revenue-maximizing price cannot exceed . On the other hand, cannot be smaller than , since otherwise a market for collaborative housing would not exist and therefore charging a smaller price could not maximize the hotels’ revenues. If , then by Table 1 hotel revenues,

are increasing and strictly convex in . Hence, we obtain that necessarily

To determine the optimal price, note first that hotel revenues are

for all , which is strictly concave on that interval. The slope of the revenues,

is negative if and only if . Hence whenever , because of the concavity of , for all it is If the first-order condition yields that . Combining the last two cases, we obtain that . Substituting this price into the expression for hotel demand yields

As a result, , concluding the proof. QED

Proof of Theorem 5. The result obtains by combining the conclusions from Theorem 1 and Theorem 4. QED

Proof of Corollary 5. By Theorem 5, the aggregate industry profits, for , are

Hence, is strictly convex there, and attains its (global) minimum at . QED

Appendix B: Notation

Table B1. Summary of notation

Notes

1. Verification costs are considered as an extension of the basic model.

2. As long as the intermediated matching probability β does not vanish, its precise value is irrelevant for our main results. We generally assume a sellers’ market where prospective renters contact hosts, who in turn approve a transaction, as it is common practice for current collaborative housing intermediaries. We show that the intermediary can capitalize on the fact that its platform increases the matching probability (see Corollary 4). For our main analysis, we neglect this effect.

3. More precisely, we assume that there are two types of hosts, or alternatively, that either host can accommodate all of the prevailing demand. For the case where the hosts have capacity constraints, equilibria are more difficult to determine, so we leave this as a topic for further research. See Osborne and Pitchik [29] for details on capacity-constrained competition in an oligopoly setting.

4. Hotels usually deal with the moral hazard problem by charging a security deposit upfront. The renter accepts those charges, because (based on the hotel’s reputation and on the renter’s agreement with the credit card company) there is a relatively simple ex post recourse procedure in the (therefore unlikely) event that a portion of the deposit is kept to cover a significant damage.

5. To be clear, ϑ = ∂/∂e|_ε=1 C(e, ϑ) = max{∂C(e, ϑ)/∂e: e ∊ [0, 1]} = max{ϑe: e ∂ [0, 1]}.

6. As long as the demand for hotels is positive, the solution to host i’s profit-maximization is isomorphic to the solution of the standard monopoly pricing problem (Tirole [44]) of finding the best price p, given a linear demand curve, a_i − bp, and marginal cost c, where a_i = (p₀ + (i – 1)ε)/(ρε), b = 1/(ρε), and c = α; see Theorem 1.

7. The idea is somewhat related to the contestable markets hypothesis by Baumol [5]: The hosts in the market set their prices so as to (ex post) prevent entry by a competitive fringe (consisting of the hotels in this case). This tactic becomes ineffective when p₀ < α + (ε /2).

8. This is analogous to the finding by Xu et al. [50] for an oligopolistic pricing game where consumers face search costs.

9. However, an increase of s is perceived strictly worse by any risk-averse renter. In our model, the renters are assumed to be risk neutral, so that any surcharge rate s beyond s* (including +∞ as the “zero tolerance” option) in Theorem 2 is equally optimal.

10. Requirement R1 can be relaxed; see the section on “Extension: Verification Cost.”

11. In other words, the hosts have no outside option as to what to do with their property, at least in the short run.

12. Hotel capacity can be aggregated via intermediaries. Online booking agents such as Expedia or Hotwire routinely offer hotel capacity in a defined area of a city and for a given quality category (star rating) at deep discounts without disclosing the name of a hotel until after the (irreversible) transaction has been completed. This corresponds to a pooled hotel capacity without branding effects, which we think of as the outside option in the collaborative housing market.

13. The hotels’ situation can be improved by reducing their commitment to the preset price; note that commitment can generally be viewed as a continuum [47]. In practice, this happens when hotels sell excess capacity through intermediaries such as Hotwire at a discount.

14. Weber [46] analyzed the special case in which all housing providers coexist and the price of the outside option is exogenous.

15. Personal communication by Roman Rochel, COO of 9Flats, Berlin, Germany, September 2013.

16. The inequality follows from the envelope theorem. For e*(L, ϑ) ∊ (0, 1), it is dφ/dL = 1 – e*(L, ϑ) > 0.

17. According to its public information as of April 2014, AirBnB had served more than 11 million guests [1].

18. An AirBnB-commissioned study by HR&A [21] showed a significant impact of intermediated collaborative housing in the San Francisco Bay Area: for example, 72 percent of AirBnB-listed properties in San Francisco (exponentially growing from about 20 in 2008 to about 40,000 in 2012) are located outside the six main hotel zip codes of the city. A personal communication with the COO of 9Flats in Berlin in 2013 revealed that it is possible to trace an increase in the price of flats to collaborative housing. Moreover, ancillary service providers are proliferating to facilitate key transfer and laundry services, effectively transforming a residential property into a commercial property.

Additional information

Notes on contributors

Thomas A. Weber

Thomas A. Weber holds the Chair of Operations, Economics and Strategy at the Management of Technology and Entrepreneurship Institute at the Swiss Federal Institute of Technology in Lausanne (EPFL). Earlier, he was a faculty member at Stanford University. He is an Ingénieur des Arts et Manufactures (École Centrale Paris) and a Diplom-Ingenieur in electrical engineering (Technical University Aachen). He holds master’s degrees in technology and policy and electrical engineering and computer science from MIT, and a Ph.D. from the Wharton School. He has been a visiting faculty member in economics at Cambridge University and in mathematics at Moscow State University. He has also served as a senior consultant with the Boston Consulting Group. His current research interests include the economics of information and uncertainty, the design of contracts, and strategy. His articles have appeared in American Economic Journal: Microeconomics, Information Systems Research, Decision Support Systems, Economics Letters, Economic Theory, Journal of Environmental Economics and Management, Journal of Mathematical Economics, Journal of Regulatory Economics, Journal of Economic Dynamics and Control, Operations Research, Theory and Decision, and other journals. He is the author of Optimal Control Theory with Applications in Economics (MIT Press, 2011).