Abstract
We develop an analytical framework of peer interaction in the sharing economy that incorporates reciprocity, the tendency to increase (decrease) effort in response to others’ increased (decreased) effort. In our model, buyers (sellers) can induce sellers (buyers) to exert more effort by behaving well themselves. We demonstrate that this joint increased effort can improve the utility of both parties and influence the market equilibrium. We also show that bilateral reputation systems, which allow both buyers and sellers to review each other, are more responsive to reciprocity than unilateral reputation systems. By rewarding reciprocal behavior, bilateral reputation systems generate trust among strangers and informally regulate their behavior. We test the predictions of our model using data from Airbnb, a popular peertopeer accommodation platform. We show that Airbnb hosts that are more reciprocal receive higher ratings and that higher rated hosts can increase their prices. Therefore, reciprocity affects equilibrium prices on Airbnb through its impact on ratings, as predicted by our analytical framework.
Similar content being viewed by others
Notes
See, for instance, https://www.airbnb.com/info/why_host.
Following a similar reasoning, we can show that the ratings on both systems positively relate to the host’s weight on reputation and that the unilateral review system responds more to the reputation weight, β_{h}.
ϕ(ω_{i}) decreasing with ω_{i} implies that guests give hosts providing worse service strictly higher ratings. ϕ(ω_{i}) constant over ω_{i} implies guests give all hosts the same rating regardless of quality.
For example, a guest may choose not to disclose her rating after a bad experience. However, a guest does not rate a bad experience better than a good one. Therefore, the rating a guest discloses still weakly reveals the quality of her experience.
To read reviews a host left for past guests, one has to: a) find out who the past guests were by looking at the host profile and checking which guests left a review for the host, b) look up the Airbnb profiles of each of these guests, and c) manually scan each guest profile to locate a review left for the guest by the host in question. We assume that the vast majority of Airbnb users do not engage in this behavior.
An alternative and equivalent way to prove proposition 2 would be to remove the term β_{i}r_{i} from the expost utility of guest i in Eq. 11 and then solve the optimization problem.
Note that since P_{1} is common knowledge, assuming r_{h, i} = v_{h} − x_{i} or r_{h, i} = v_{h} − x_{i} − P_{1} is exactly the same for our analysis.
Note that even under the assumption that hosts are able to infer guests’ 𝜃, all hosts, and in particular professional hosts, who have a higher weight on reputation would select those guests with higher 𝜃 in order to reduce the probability of receiving a lower rating.
References
Anderson, M., & Magruder, J. (2012). Learning from the crowd: Regression discontinuity estimates of the effects of an online review database. The Economic Journal, 122(563), 957–989.
Andreoni, J. (1990). Impure altruism and donations to public goods: a theory of warmglow giving. The Economic Journal, 100(401), 464–477.
Blanchard, S.J., Carlson, K.A., Hyodo, J.D. (2016). The favor request effect: Requesting a favor from consumers to seal the deal. Journal of Consumer Research, 42(6), 985–1001.
Charness, G. (2004). Attribution and reciprocity in an experimental labor market. Journal of Labor Economics, 22(3), 665–688.
Dellarocas, C., & Wood, C.A. (2008). The sound of silence in online feedback: Estimating trading risks in the presence of reporting bias. Management Science, 54 (3), 460–476.
Edelman, B. (2017). The market design and policy of online review platforms. Oxford Review of Economic Policy, 33(4), 635–649.
Einav, L., Farronato, C., Levin, J. (2016). Peertopeer markets. Annual Review of Economics, 8, 615–635.
Falk, A., & Fischbacher, U. (2006). A theory of reciprocity. Games and Economic Behavior, 54(2), 293–315.
Farronato, C., & Fradkin, A. (2018). The welfare effects of peer entry in the accommodation market: The case of Airbnb. Tech. rep., National Bureau of Economic Research.
Fehr, E., & Gächter, S. (2000). Fairness and retaliation: The economics of reciprocity. Journal of Economic Perspectives, 14(3), 159–181.
Fradkin, A., Elena G., David H. (2017). The determinants of online review informativeness: Evidence from field experiments on Airbnb.
Godes, D., & Silva, J.C. (2012). Sequential and temporal dynamics of online opinion. Marketing Science, 31(3), 448–473.
Gouldner, A.W. (1960). The norm of reciprocity: a preliminary statement. American Sociological Review, 25(2), 161–178.
Horton, J. (2015). Reputation inflation: Evidence from an online labor market.
Kahneman, D., Knetsch, J.L., Thaler, R. (1986). Fairness as a constraint on profit seeking: Entitlements in the market. The American Economic Review, 76 (4), 728–741.
Levine, D.K. (1998). Modeling altruism and spitefulness in experiments. Review of Economic Dynamics, 1(3), 593–622.
Luca, M. (2016). Reviews, reputation, and revenue: The case of Yelp.com.
Malmendier, U., Velde, V.L.T., Weber, R.A. (2014). Rethinking reciprocity. Annual Review of Economics, 6(1), 849–874.
Rabin, M. (1993). Incorporating fairness into game theory and economics. The American Economic Review, 83(5), 1281–1302.
Resnick, P., & Zeckhauser, R. (2002). Trust among strangers in internet transactions: Empirical analysis of ebay’s reputation system. The Economics of the Internet and Ecommerce. Emerald Group Publishing Limited, 127–157.
Rotemberg, J.J. (2006). Altruism, reciprocity and cooperation in the workplace. Handbook of the economics of giving, altruism and reciprocity, 2, 1371–1407.
Seiler, S., Yao, S., Zervas, G. (2018). Causal inference in wordofmouth research. Methods and results.
Sobel, J. (2005). Interdependent preferences and reciprocity. Journal of Economic Literature, 43(2), 392–436.
Tadelis, S. (2016). Reputation and feedback systems in online platform markets. Annual Review of Economics, 8(1), 321–340.
Yoganarasimhan, H. (2013). The value of reputation in an online freelance marketplace. Marketing Science, 32(6), 860–891.
Zervas, G., Proserpio, D., Byers, J. (2015). A first look at online reputation on airbnb, where every stay is above average.
Zervas, G., Proserpio, D., Byers, J.W. (2017). The rise of the sharing economy: Estimating the impact of airbnb on the hotel industry. Journal of Marketing Research, 54(5), 687–705.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix A: Proofs
1.1 A.1 Proof of proposition 1
Proposition 1
The host’s average rating on Airbnb is positively related to her reciprocity weight, i.e.,∀α_{i} ≥ 0 and α_{i}≠ 0,
where
is the average rating of the host.
Proof
We solve the subgame equilibrium at Period 2. Note that at Period 2, both players choose their optimal effort level as the best response to the other’s effort. Then each player reports their utility of accommodation in the rating.
Plugging r_{h, i}(e_{i}, e_{h}) = v_{h} + α_{i}u(e_{i}, e_{h}) and r_{i}(e_{i}, e_{h}) = v_{i} + α_{h}u(e_{i}, e_{h}) into the expost utility of host and guest i, we have:
Combining the first order conditions of the two optimality problems, we have:
where \(A\equiv \left (\frac {k}{c_{i}}\right )^{\frac {1k}{2}}\left (\frac {1k}{c_{h}}\right )^{\frac {1+k}{2}}\) and \(B\equiv \left (\frac {k}{c_{i}}\right )^{1\frac {k}{2}}\left (\frac {1k}{c_{h}}\right )^{\frac {k}{2}}\).
Thus,
From the above, we have:
and since \(R_{airbnb}\equiv \int r_{h,i}di\),
□
1.2 A.2 Proof of proposition 2
Proposition 4.2
The ratings on both review systems depend positively on the weights of reciprocity and reputation, α_{h} and β_{h}.However, given the same pool of guests, the host’s average rating on Airbnb responds more to the reciprocity weight, while the rating on the unilateral review system responds more to reputation weight, i.e.:
where \(R_{airbnb}\equiv {\int }_{i}r_{h,i}^{air}(e_{h},e_{i}) di\) is the host’s average rating on Airbnb, and \(R_{uni}\equiv {\int }_{i}r_{h,i}^{uni}(e_{h},e_{i}) di\) is the host’s average rating on an unilateral review system.
Proof
From previous results, we have:
For the same host and the same guest pool on both the unilateral review system platform and Airbnb, and given identical values of the parameters, except β_{i} = 0 under the unilateral review system, we have:
Since \(R_{airbnb}\equiv {\int }_{i}r_{h,i}^{air}(e_{h},e_{i}) di\) and \(R_{uni}\equiv {\int }_{i}r_{h,i}^{uni}(e_{h},e_{i}) di\), we have:
Thus, under a unilateral reputation system, hosts that care more about reputation are ranked higher than hosts that care more about the shared experience utility. The opposite is true on bilateral reputation systems like Airbnb.^{Footnote 10}□
1.3 A.3 Proof of proposition 3
Proposition 3
On Airbnb, prices increase after a positive shock on rating and decrease after a negative shock on ratings. Given the same price P _{1} at period 1, and ratings R _{ a i r b n b } and \(R^{\prime }_{airbnb}\) disclosed at period 2, we have the following relationship for prices posted at period 3:
Proof
Exante, guests determine whether to enter the market according to V _{i}(P). Guest i enters the market if and only if V _{i}(P) ≥ 0, given P. Therefore, the marginal guest is guest i^{∗} where \(V_{i^{*}}(P)= 0\). For each guest i at period 3, the expected utility V _{i}(P) is positively determined by her inference of α_{h}, β_{h}.
From previous results, we have \(\frac {\partial u(e_{i},e_{h})}{\partial \alpha _{h}}>0\) and \(\frac {\partial u(e_{i},e_{h})}{\partial \beta _{h}}>0\). Together with r_{i} = v_{i} + α_{h}u(e_{i}, e_{h}), we have:
Then, since U_{i}(e_{i}, e_{h}, r_{i}, v_{h}) = v_{h} + α_{i}u(e_{i}, e_{h}) + β_{i}r_{i}, we have that ∀(α_{i}, β_{i}) > 0,
where u(e_{i}, e_{h}) is the shared experience utility and U_{i}(e_{i}, e_{h}, r_{i}) is expost utility of guest i during the accommodation stay.
At period 3, V _{i}(P_{3}) is the exante utility of the guest i if she decides to transact with the host. The guest i forms her expectation based on the publicly observed price, P_{3}, and the average rating of the host, \(R_{h}\equiv \int r_{h,j} dj\), i.e.:
where F^{updated}(Ψ_{h}) is the posterior distribution of the host’s characteristic parameter vector (α_{h}, β_{h}, v_{h}). The Bayesianupdated guests update the prior distribution F(Ψ_{h}) upon the signal R_{h} to derive F^{updated}(Ψ_{h}) .
From Eqs. 40, 41, and 42, we have that ∀(α_{h}, β_{h}, v_{h}) ∈Ψ_{h}, the expected value of U_{i}(e_{i}, e_{h}, r_{i}, v_{h}) are positively related to α_{h} and β_{h}, i.e.,
The two conditions above imply that the exante utility to transact is higher if the host is perceived to have higher weight on shared experience or reputation, respectively.
Meanwhile, from previous results, we have:
Conditions (45) and Eq. 46 show that the hosts with higher value of α_{h} and β_{h} have higher rating r_{h, i} given the same guest i. Then, from \(R_{h}\equiv \int r_{h,i} di\), we have that, given the same guest pool, the average rating, R_{h}, reveals a higher value of (α_{h}, β_{h}).
Suppose that two hosts are identical, except for their ratings, i.e., they have the same price P_{1}, same location, and similar property, but \(R_{airbnb}> R^{\prime }_{airbnb}\). Then the higher rating R_{airbnb} is a positive signal relative to \(R^{\prime }_{airbnb}\), i.e., the expected value of the host’s characteristics is better for the host with R_{airbnb}. Thus, if the two hosts post identical P_{3}, the expected demand toward the host with higher average ratings would be higher, i.e., \(Q(P_{3}, R_{airbnb})>Q(P_{3},R^{\prime }_{airbnb})\).
Since each period3 guest is more willing to transact with a host having R_{airbnb} than with a host having \(R^{\prime }_{airbnb}\), the host with the higher rating posts higher price P_{3} in this monopolistic pricing setting (assuming that the hosts are faced with the same pool of guests).
Formally, let’s suppose P_{1} and Q_{1} are the same for Host A and Host B, and, without loss of generality, assume the mass of guests enter the market have the same set of parameters, (α_{i}, β_{i}). Let Host A have an average rating R_{airbnb} and Host B an average rating \(R^{\prime }_{airbnb}\). If \(R_{airbnb}>R^{\prime }_{airbnb}\), then from Eqs. 38 and 39, at least one of the following conditions holds:
Then, for any positive P_{3},
The marginal guest is defined as the one with V _{i}(transactP_{3}, R_{airbnb}) = 0. Then, from Eq. 47, we know that the marginal guest transacting with Host A can bear a higher P_{3} compared to that trading with Host B, since Host A is expected to have higher value of α or β or both.
Since P_{3} is determined by:
we have that, given that Ψ_{g} is the same for Host A and B, \(P_{3}(R_{airbnb})>P_{3}(R^{\prime }_{airbnb})\). □
1.4 A.4 Relaxing the truthtelling assumption
As defined in Section 3.3, we have that:
Plugging the equation above into \(R_{airbnb}\equiv \int r_{h,i}di\), we have:
Now, assume all hosts are faced with an identical pool of guests. Let ω_{i} ≡ v_{h} + u(e_{i}, e_{h}). From previous results, we have:
Since ϕ is a weakly increasing mapping, we have
The inequality is strict for some ω_{i}.
From Eqs. 51 and 52, we have \(\frac {\partial \phi (\omega _{i})}{\partial \alpha _{h}}\geq 0\) and the inequality is strict for some ω_{i}, i.e.:
Appendix B: Alternative models
1.1 B.1 A Simple model
We start with a simple model where we assume the host to be a riskneutral profit maximizer. The service quality offered by the host is exogenously given and fixed across transactions. Further, the service quality is private information of the host and only revealed to the guests during their stay in the host’s property. The distribution of service quality is common knowledge. We assume a monopolistic host and a continuum of guests with heterogeneous tastes. The guests are located on a line and the host is located at the center. The heterogeneous taste of guest i is modeled as x_{i}, which denotes the distance between the host and the guest i, and it follows a uniform distribution over [0, 1]. Without loss of generality, we assume the effort cost of publishing a review is zero. The timing of the game is as follows:

in Period 1, the host posts price P_{1} and a continuum of guests – the early guests – enter the market. The early guests can only observe P_{1}. As stated above, the expected value of service quality, E[v_{h}], is common knowledge. Guests decide whether to request accommodation. The transaction volume for this set of guests, Q_{1}, is realized.

in Period 2, the accommodation stay takes place. Service quality is now revealed to the guest who requests the accommodation. The utility of guest i is v_{h} − x_{i}. At the end of this period, the guest i publishes a rating r_{h, i} for the host.

in Period 3, the host observes the ratings received in period 2 and post a new price P_{3}. A continuum of guests – the late guests – enter the market. Their heterogeneous taste parameter x_{i} follows the same distribution of the early guests. They observe the average rating for host h disclosed in Period 2 and the price P_{3}. They make their accommodation decision accordingly.
We assume that guests truthfully report their utility in the ratings, i.e., r_{h, i} = v_{h} − x_{i}, where v_{h} denotes the service quality and x_{i} denotes the heterogeneous taste of guest i. We don’t consider this truthtelling assumption is a strong one here, since under this scenario, an agent does not have an incentive to collude with the host in inflating ratings. Meanwhile, if agents truthfully report service quality in the ratings, informative ratings have value to other users on the platform. Thus, the truthtelling assumption is justified by the phenomenon of “warm glow” discussed in Andreoni (1990)^{Footnote 11}
Moreover, we assume that the distribution of v_{h} and x_{i} is common knowledge and, hence, E[v_{h}] is known exante to the guests and E[x_{i}] is known exante to the host.
In this setting, the only choice variable of the host is price. The objective function of the host is given by:
where P denotes price and Q denotes the transaction volume. V _{h}(P) denotes the exante utility contingent on choosing price P. Since the host is riskneutral and only interested in expected profits, the utility function coincides with expected profits.
Similarly, the only choice variable of a guest is whether to request accommodation. A guest requests accommodation from the host if and only if her expected utility from the accommodation is nonnegative. The guest’s exante utility prior to the accommodation is given by:
where V _{i}(transactP) is the exante utility of the guest i if she books the accommodation. P denotes the price set by the host, v_{h} denotes the service quality, and x_{i} denotes the heterogeneous taste of guest i. we assume x_{i} to have uniform distribution over [0, 1].
After staying in the host’s property, the guest i publishes a rating r_{h, i} = v_{h} − x_{i}. The host’s rating \(R\equiv \int r_{h,i} di\) depends only on v_{h} and E[v_{h}] as E[v_{h}] determines the pool of guests requesting accommodation from the host.
In the solution below, we solve backwards for Perfect Bayesian Equilibrium.
Proof
In the first period, early guests make a decision based on E[v_{h}], which is common knowledge. When the host chooses P_{1}, the marginal guest i^{∗} who is indifferent about reserving the accommodation or not, is given by:
Guests with \(x\in [0,x_{i^{*}}]\) book the accommodation. Hence, the first period transaction volume is:
Now let’s consider the rating a host receives. The average rating, denoted by R, is given by:
Since both R and Q_{1} are common knowledge in Period 3, late guests can infer the value of v_{h} from \(v_{h}=R+\frac {Q_{1}}{2}\). Therefore, the marginal guest in Period 3 is given by \(v_{h}x_{j^{*}}P_{3}= 0\), i.e.,
Hence, the host maximizes profits in Period 3 by solving the following optimality problem:
From the first order condition (FOC), we have \(P_{3}^{*}=\frac {v_{h}}{2}\). Then in Period 1, assuming hosts discount future revenue at rate β, a host solves:
From the FOC, we have:
Then, from Eqs. 57 and 62, we have \(Q_{1}=\frac {E[v_{h}]}{2}\). Thus, we have:
For a pool of hosts with \(v_{h}\in [\underline {v}_{h},\bar {v}_{h}]\), the average value of v_{h} is E[v_{h}]; hence, the average ratings of hosts is \(M=\int R_{j}dj=\frac {3}{4}E[v_{h}]\).
Let R_{c} denote the rating casual hosts and R_{p} denote the rating of professional hosts. For R_{c} to be systematically higher than R_{p}, we have to assume that the average service quality of casual hosts is higher than that of professional hosts, i.e., \(E\left [{v_{h}^{c}}\right ]>E\left ({v_{h}^{p}}\right )\), where \(E\left [{v_{h}^{c}}\right ]\) and \(E\left [{v_{h}^{p}}\right ]\) denote the average service quality of casual hosts and of professional hosts, respectively. Note that casual and professional hosts differ in their market participation frequency. In this simple model, the service quality of the host is not endogeneously chosen by the host, hence we lack a mechanism to link a host’s market participation frequency with their ratings. Thus, in order for \(E\left [{v_{h}^{c}}\right ]>E\left [{v_{h}^{p}}\right ]\), we need to assume that market participation negatively correlates with the exogenously given service quality. However, this does not seem to be a natural assumption to make. As higher service quality can translate into higher ratings that attracts future business, hosts choosing to participate more frequently should not have less incentive to work hard toward achieving high ratings. If anything, this rationale suggests that market participation frequency should be positively correlated with service quality. We conclude that this simple model cannot easily explain why professional hosts have lower ratings. □
1.2 B.2 Relaxing the truthtelling assumption
Next, motivated by the observation that the guests who do not report ratings are likely to have had a worse experience (Fradkin et al. 2017), we relax the truthtelling assumption. In doing so, we allow selection bias in ratings. To allow for selection bias, we assume that guests provide a rating to a host only if the rating is above a threshold 𝜃_{i}, i.e.:
Then the exante utility of the guest i in period 1 is given by:
where r_{h, i} denotes the rating guest i gives to the host and r_{i} denotes the rating the host gives to the guest i. The term α_{i} denotes the weight of the host’s reputation in guest i’s utility.
Compared with the guest’s expost utility in the simple model (55), the current utility function has two new parts. The first part includes 1{rating}(v_{h} − x_{i}) − r_{h, i} and the rating threshold 𝜃_{i}. The difference between the disclosed rating and the true level of the guest’s utility captures the guest’s disutility derived from reporting a rating different from the true value of service quality and deteriorating rating informativeness. The term 𝜃_{i} captures the cost (e.g., psychological cost) for a guest to give a low rating. Together, these terms capture the tradeoff faced by the guest when choosing whether to rate a host and what rating to disclose. While psychological costs may encourage guests to inflate ratings, guests also have an incentive to provide informative ratings as a contribution to other users on the platform. The two forces work in opposite direction and together determine the rating guests report.
The second part is r_{i}, the rating guest i receives from the host, which captures the fact that the guest i has reputation concerns. The reason for r_{i} to be part of the guest’s utility is to match the Airbnb setting, where a host can rate the guest, and this rating affects whether future hosts will accept the guest’s accommodation request.
In all our analyses, we only consider ratings produced under the new simultaneous Airbnb reputation mechanism. Therefore, strategic rating manipulation of ratings is not a concern, i.e., hosts cannot strategically collude with guests to exchange high ratings, which implies that r_{i} is not a function of r_{h, i}.
In the equilibrium of this model, a host receives a higher rating than in the simple model, and the inflated ratings depend on the average level of 𝜃_{i} associated with the pool of the guests. While 𝜃_{i} may be affected by the interaction between guests and hosts, it seems unlikely that it is also correlated with market participation, since this information is not revealed to guests. Unless we are willing to assume such a correlation, we cannot easily explain the difference in ratings observed in Why do casual hosts have higher ratings than professionals?. The formal proof of this statement is as follows.
Proof
Under this model, the only choice variable of the guest during Period 2 is r_{h, i}. If guest i decides to request the accommodation, her exante utility in Period 1 is given by:
The expost utility of guest i at the end of Period 2 is given by:
With respect to the best response of guest i, two options exist:

1.
If r_{h, i} ≥ 𝜃_{i}, then:
$$ V_{i}(transactP)=E[v_{h}]x_{i}P+E[r_{i}\alpha_{i}r_{h,i}(v_{h}x_{i})] $$(68)$$ u_{i}(r_{h,i})= [v_{h}x_{i}+r_{i}\alpha_{i}r_{h,i}(v_{h}x_{i})] $$(69)where u_{i}(r_{h, i}) is the expost utility after the accommodation stay. Then, from Eq. 69 and α_{i} > 0, we have:
$$ r_{h,i}=v_{h}x_{i}. $$(70) 
2.
If r_{h, i} < 𝜃_{i}, then, the guest i does not publish a rating.
Then, the exante utility for a guest to enter the market is given by:
Note that under simultaneous ratings, guest i cannot directly influence r_{i} by choosing the rating she gives to the host. Thus, the only choice of guest i in Period 1 is to transact if and only if E[v_{h}] − x_{i} − P ≥ 0. Therefore, the following conditions still hold: \(Q_{1}=x_{i}^{*}=E[v_{h}]P_{1}\) and \(P_{1}=\frac {E[v_{h}]}{2}\).
Then, the average rating of a host under this model, denoted as R^{biased}, is:
where x^{∗∗}≡ min{v_{h} − 𝜃_{i}, E[v_{h}] − P_{1}}, and f is the density function of x_{i}.
Then, denoting the average rating in the simple model as \(R^{unbiased}\equiv \frac {{\int }_{i}r_{h,i}di}{{\int }_{i}idi}\), we have that:
i.e., the average rating under selection bias is higher than the average rating without selection bias, and their difference is a function of 𝜃. Under this condition, to observe systematically lower ratings for professional hosts, we need to assume that \({v_{h}^{p}}\) is systematically lower than \({v_{h}^{c}}\) or that the distribution of \({v_{h}^{c}}\) first order stochastically dominates (FOSD) the distribution of \({v_{h}^{p}}\).
Alternatively, to explain the rating patterns observed, we could assume that guests of professional and casual hosts differ systematically in their 𝜃, the psychological cost of leaving a bad review. Specifically, guests of professional hosts must have a systematically lower psychological threshold than guests of casual hosts. However, guests cannot observe hosts market participation and, thus, they cannot discern between professional or casual hosts; and hosts cannot infer the guests’ 𝜃, so they cannot select a specific type of guest. Thus, this selfselection of guests depending on the host type (and vice versa) is unlikely to occur in practice.^{Footnote 12}□
1.3 B.3 Relaxing the risk neutral assumption
In this section, we relax the riskneutral assumption and allow the behavior of the guests to enter into the utility function of the host. We propose this modification because of the nature of Airbnb transactions. Since Airbnb hosts share their own properties, it is natural to expect them to be riskaverse toward guest misconduct.
Formally speaking, we assume the effort of guest i, denoted as e_{i}, to enter into the utility of the host, and the host’s utility is assumed to be concave with respect to e_{i}. The utility function of the host is given by:
where, as before, P denotes price, Q denotes the transaction volume, and v_{h}(P) denotes the exante utility contingent on choosing price P. r_{h, i} is the rating the host receives from the guest i. The term u_{h}(e_{i}) shows that the guest’s effort e_{i} affects the host’s welfare. The concavity of u_{h} captures the risk aversion of the host. Then, hosts trade off expected profits against the possibility of guest misconduct in accepting guests. While this assumption reduces the number of guests a host will accept, the host’s rating does not affect service quality since it is still exogenously given and fixed. Formally, the only choice variable is still P and the optimality problem of the host is reduced to:
Independently of which assumptions are invoked on r_{h, i}, the absence of strategic manipulation of r_{h, i} makes it impossible to alter the optimality problem, which therefore is analogue to the simple model discussed above.
Moreover, since service quality is exogenously given in this scenario, to explain the systematically lower ratings to professional hosts, we would need to assume that the service quality of casual and professional hosts follow different distributions and that the distribution of \({v_{h}^{c}}\) FOSD the distribution of \({v_{h}^{p}}\).
1.4 B.4 Endogenous service quality
Next, we relax the exogenous service quality assumption. We allow service quality to vary between transactions. This assumption is consistent with the high heterogeneity of service quality on Airbnb. In this scenario, we consider three alternative models.
1.4.1 B.4.1 Model I: Hosts only care about profit and reputation
First, we endogenize service quality without changing the assumption that hosts care only about profit and reputation. The optimality problem of the host in Period 1 is given by:
Demand is realized in Period 1 while only reputation concerns and effort cost determine effort levels in Period 2. Then, the host’s optimality problem in Period 2 is:
Because of their higher market participation, professional hosts have a higher weight on reputation concerns, i.e., professional hosts have systematically higher β_{h}. With the assumption that guests report hosts’ effort levels in ratings r_{h, i}, i.e., r_{h, i} = e_{h}.
From the FOC, we have:
The above condition solves for the optimal level of \(e_{h}^{*}\).
If the effort cost function is identical across hosts, i.e., the function C_{p}(e_{h}) = C_{c}(e_{h}) ≡ C(e_{h}) for all e_{h}, and effort costs increase with effort level, i.e., C^{′}(e_{h}) > 0,∀e_{h}, then professional hosts exert higher effort levels due to their higher β_{h}, i.e., from β_{p} > β_{c} and \(C^{\prime }_{h}>0\), we have \(e_{p}^{*}>e_{c}^{*}\).
Even if the effort cost function of professional hosts is systematically different from that of casual hosts, because of economies of scale, it is unlikely that the latter have systematically lower marginal effort cost than professional hosts.That is, C^{′}(e_{p}) ≤ C^{′}(e_{c}) for each e_{h}. Even if we assume C^{′}(e_{p}) > C^{′}(e_{c}) for some e_{h}, the difference in marginal effort cost has to be large enough to offset the effect of β_{h} so that casual hosts can exert systematically higher effort under this model. Therefore, this model cannot easily explain why professional hosts have lower ratings.
1.4.2 B.4.2 Model II: Hosts also care about guest behavior
In this model, hosts also care about guest behavior. Hosts on Airbnb are relatively “small” service providers compared to firms in the accommodation industry, such as Hilton or Marriott. Therefore, a natural assumption is that hosts are risk averse with respect to possible guest misconduct. We model this by letting guest conduct enters hosts’ utility function. However, as we show, simply introducing guest conduct in the utility function of a risk averse host does not suffice to explain why professional hosts have lower ratings than casual hosts. Formally speaking, if we assume e_{i} and e_{h} are separable in the host’s utility, guest behavior cannot alter the host’s effort. Thus, we have to further assume a nonseparable function of e_{h} and e_{i} as we do in our main model.
As U_{h} takes a seperable functional form of e_{i} and e_{h}, without loss of generality, we assume U_{h} is given by:
where g(e_{i}) captures the effect of guests’ conduct on the host’s utility, and the concavity of g(⋅) models the host’s risk averse attitude toward the guest misconduct.
Assuming r_{h, i} = e_{h}, we have the same FOC as the previous model, i.e., \(C^{\prime }_{h}(e_{h})^{*}=\beta _{h}\). This means that e_{i} does not determine the optimal level of e_{h} and therefore it cannot explain the difference in ratings between casual and professional hosts.
1.4.3 B.4.3 Model III: Hosts have interdependent preference
Next, we assume that the host has interdependent preference (without assuming the reciprocity feature discussed in our main theoretical framework), i.e., the utility of guest i, denoted as U_{i}, enters into the host’s utility function.
Under this assumption, the optimality problem of the host is given by:
where U_{i} is the expost utility of guest i given by U_{i}(e_{i}, e_{h}, r_{i}) = f(e_{h}) − C_{i}(e_{i}) + β_{i}r_{i}. Also, e_{i} and e_{h} are the efforts of guest i and the host h, respectively. The function g(⋅) denotes how much hosts care about a guest’s behavior, and f(⋅) denotes guest utility derived from host’s effort.
To derive a closedfrom solution of the optimal effort level, we assume \(f(e_{h})=e_{h}^{1k}\) and \(g(e_{i})={e_{i}^{k}}\), and the effort cost function to be quadratic, i.e., \(C(e_{h})=\frac {c_{h}}{2}{e_{h}^{2}}\).
After invoking r_{i} = g(e_{i}), r_{h, i} = f(e_{h}), we have:
Then, we have \(e_{h}^{*}=\left (\frac {(1k)(\alpha _{h}+\beta _{h})}{c_{h}}\right )^{\frac {1}{k + 1}}\) and \(\frac {\partial e_{h}^{*}}{\partial \beta _{h}}>0\).
If casual hosts differ from professional hosts only in β_{h}, and professional hosts have a higher level of β_{h}, we have \(e_{p}^{*} > e_{c}^{*}\). Therefore, \(r_{h,i}^{c}<r_{h,i}^{p}\), ∀i. Thus, the average rating of professional hosts is expected to be higher than casual hosts, contradicting what we observe in the Airbnb data.
In order to explain the systematically lower ratings of professional hosts, we need an additional assumption. Specifically, we need to assume that casual hosts are systematically more altruistic than professionals. This assumption can be implemented by adding the parameters α^{g} in front of the interdependent utility term in the gross utility of the host and assuming that the difference on the altruism weights are larger than the difference between reputation weights. Formally stated:
where α_{c} and α_{p} are the weights on guests’ utility of the nonprofessional hosts and the professional hosts, respectively.
By invoking this assumption, we allow casual hosts to have systematically higher intrinsic altruism, and the difference between altruistic attitude is large enough to offset the difference between reputation concerns. However, we consider altruistic behavior to be a larger departure from standard assumptions and our explanation based on reciprocity to be more natural for the setting of Airbnb.
Rights and permissions
About this article
Cite this article
Proserpio, D., Xu, W. & Zervas, G. You get what you give: theory and evidence of reciprocity in the sharing economy. Quant Mark Econ 16, 371–407 (2018). https://doi.org/10.1007/s1112901892019
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s1112901892019