bilateral ratings and p2p market competition and segmentationpeople.bu.edu/monic/p2p.pdf ·...

Bilateral Ratings and P2P Market Competition andSegmentation

T. Tony Ke1 Baojun Jiang2 Monic Sun3

1MIT

2Washington University in St. Louis

3Boston University

April 26, 2017

Guanghua School of Management, Peking University

Ke, Jiang and Sun P2P Market Competition and Segmentation April 26, 2017

P2P Platforms


Unilateral Ratings on Traditional Platforms


Bilateral Ratings at Airbnb

Our community is built on a great deal of trust—trust that makes hostsfeel comfortable allowing travelers to stay in their home, and trust thathelps travelers feel like they belong anywhere. The foundation of thattrust is our review system.For each guest review, a host is asked to give a star rating for the guest’scleanliness and communication. Airbnb allows hosts to pick and choosethese strangers by publishing guest profiles and reviews.


Bilateral Ratings at Lyft

After each ride, you have the opportunity to rate your driver, and they willrate you. Before a ride, you’ll be able to see your driver’s rating and they’llbe able to see yours. Lyft has rigorous standards for drivers, and eachrating you give can have an impact on that driver’s future with Lyft. Inaddition, passengers with a low star rating may have a harder time gettinga Lyft.


Research Questions

How does the availability of rating of consumers affect thecompetitive landscape?

How do prices change when such ratings are available?

Among platforms, service providers and consumers, who benefit fromthe bilateral rating system?


Literature Review

Competitive search in labor markete.g., Montgomery (1991), Peters (1991), Burdett, Shi and Wright(2001), Shi (2002), Shimer (2005)

Behavior-based discriminatione.g., Fudenberg and Villas-Boas (2006), Pazgal and Soberman(2008), Shin and Sudhir (2010), Shin (2012)

P2P markete.g., Einav, Farronato and Levin (2016), Romanyuk (2016), Arnosti,Johari and Kanoria (2015), Farajallah, Hammond and Penard (2016)


Preview of Results

Compared with unilateral ratings, bilateral ratings may lead to higherprices, and thus lower consumer surplus.

Consumers with good ratings apply to only high-quality serviceproviders, and expect a higher utility; while consumers with badratings apply to both high-quality and low-quality service providers,and expect a lower utility.


MODEL


Service Providers

……

!

"!#$

1 − " !#'

M service providers are distinguished by service quality, withγ ∈ (0, 1) in high quality qH , and 1− γ in low quality qL ≤ qH .

Marginal cost of service provision is normalized as zero.


Consumers

…

(

) (

*

N consumers distinguished by serving cost, with f (θ) positive andfinite for θ ∈ [0, θ̄].

To serve a consumer of cost type θ, a service provider of quality qincurs cost θg(q), where g(·) > 0 and g ′(·) ≥ 0.

e.g., g(q) = 1. g(q) = q.

Consumption utility of quality q and price p is u(p, q) = q − p.


Rating System

Bilateral ratings: both service providers’ quality q and consumers’cost type θ are common knowledge (main model).

Unilateral ratings: only service providers’ quality q is commonknowledge; a consumer’s cost type θ remains her private information(extension).


Matching Game

……

…

+$, +$- +$./ +', +'- +' ,0. /

1 Service providers post prices.

Service providers can commit to their posted prices.Prices do not depend on θ.

2 Consumers submit applications. One per person.

3 Service providers make offers. One per person → lowest θ at hand.

4 Trade and payoffs realize. Zero payoff for no matches. Matchingplatform charges δ percent commission for each matched transaction.


Market Frictions

Where do frictions come from in this model?

Coordination frictions—multiple consumers apply for the sameservice provider; meanwhile, some service providers receive noapplications.

Allow unmatched agents play the same matching game again → somemore will get matched→ lower coordination frictions and mismatches.

We only consider one-shot game.

Multiple-round matching games are difficult to analyze.Mismatches and market frictions are both important in reality andinteresting in theory.


Large Market and Symmetric Equilibrium

M,N →∞, and 0 < n ≡ N/M <∞.

We only consider symmetric strategy:

Service providers of the same type post the same price.

pH1 = · · · = pHγM = pH ,

pL1 = · · · = pL(1−γ)M = pL.

Consumers of the same type use the same mixed application strategy.aj(θ) is the probability a consumer applies to one particular serviceprovider of type j ∈ {H, L}.


EQUILIBRIUM ANALYSIS


Consumers’ Problem: Application Strategy

Normalization condition:

γMaH(θ) + (1− γ)MaL(θ) = 1.

aj(θ)→ 0, as M →∞.

Introduce queue length of a service provider of type j asxj(θ) ≡ Nf (θ)aj(θ).

γxH(θ) + (1− γ)xL(θ) = nf (θ).

xj(θ)→ finite, as N,M →∞.


Consumers’ Problem: Acceptance Rate

Acceptance probability of consumer θ by a service provider of type jconditional on the consumer applied to this service provider:

bj(θ) = limN→∞

θ∏t=0

(1− aj(t))Nf (t)dt

= limN→∞

θ∏t=0

(1−

xj(t)

Nf (t)

)Nf (t)dt

=θ∏

t=0

e−xj (t)dt

= e−∫ θ

0 xj (t)dt .

bj(θ) decreases with θ, i.e., consumers with higher serving cost expecta lower acceptance rate.


Consumers’ Problem: Expected Utility

Let U(θ) be the maximum expected utility of consumer θ.

A consumer of type θ submits an offer to a service provider of type jwith positive probability if and only if bj(θ)(qj − pj) = U(θ).

xj(θ)

{> 0, if bj(θ)(qj − pj) = U(θ),= 0, if bj(θ)(qj − pj) < U(θ).

Consumers’ tradeoff in application: everyone prefers higher qj − pjbut service providers with higher qj − pj are more competitive andthus have lower acceptance rate bj(θ).


Characterization of Consumers’ Application Strategy

!

"# − %#"& − %&

'()

'*(+*)

1

0 !̅!# !&

apply to H with /#(!) > 0 apply to L with /&(!) > 0


Characterization of Consumers’ Application Strategy

If 1 < qH−pHqL−pL < e

nγ , consumers with type θ ∈ [0, θH ] apply to service

providers of high quality only, and consumers with θ ∈(θH , θ̄

]apply

to both types of service providers. For θ ∈[0, θ̄],

xH(θ) =

{ nγ f (θ), 0 ≤ θ ≤ θHnf (θ), θH < θ ≤ θ̄ ,

xL(θ) =

{0, 0 ≤ θ ≤ θHnf (θ), θH < θ ≤ θ̄ ,

U(θ) =

(qH − pH)e−nγF (θ)

, 0 ≤ θ ≤ θH(qH − pH)

(qH−pHqL−pL

)−(1−γ)e−nF (θ), θH < θ ≤ θ̄

.

Other cases can be similarly characterized.


Service Providers’ Problem: Profit Function

Consider an individual service provider of type j , who deviates to postprice p0

j .

As M →∞, this deviation imposes no impact on U(θ).

If U(θ) < qj − p0j , consumers of type θ will apply to this service

provider until b0j (θ)(qj − p0

j ) = U(θ), where b0j (θ) is this service

provider’s acceptance rate for a consumer of type θ. Otherwise,consumers of type θ will not apply to this service provider.

b0j (θ) =

U(θ)

qj − p0j

for θ ≥ θ0 =

{0, qj − p0

j ≥ U(0),

U−1(qj − p0j ), otherwise.

The service provider’s profit function under full market coverage:

π0j (p0

j ; pH , pL) =

∫ θ̄

θ0

[(1− δ)p0

j − θg(qj)]·

[−db0

j (θ)

dθ

]dθ.


Service Providers’ Problem: Optimality Condition

Concavity condition: a pure strategy Nash equilibrium (p∗H , p∗L)

exists if π0j (p0

j ; pH , pL) is concave.

This imposes some lower bound on nf (·). We will restrict our attentionto uniform distribution only, where f (θ) = 1/θ̄.

Optimality condition: a pure strategy Nash equilibrium (p∗H , p∗L) is

determined by,

p∗j = arg maxp0j

π0j (p0

j ; p∗H , p∗L), for j ∈ {H, L}.


EQUILIBRIUM IMPLICATIONS


Equilibrium

Theorem

Under the concavity condition and uniform distribution of F (·),

there always exist infinite number of pure-strategy Nash equilibria,which satisfy qH − p∗H = qL − p∗L = ε for ε ∈ (0, ε̄];

in the case that g(q) = 1 or g(q) = q, all equilibria satisfy thatqH − p∗H ≥ qL − p∗L.

As a parallel with Diamond Paradox, competitive firms gain monopolypower in a homogeneous product market with coordination frictions.

After adjusting for price, high quality service providers are morepreferred in equilibrium.


Equilibrium Prices

g (qH ) θ_

1-δqH-(qL-

g (qL ) θ_

1-δ)

qH

g (qL ) θ_

1-δ

qL

pH*

pL*

Figure: Equilibrium prices under the parameter setting that n = 1, γ = 0.5,qH = 2qL, δ = 0.1, θ̄ = 0.2qL, and g(q) = 1.


Equilibrium Market Segmentations

!

"# − %#"& − %&

'()

1

0 !̅!#

apply to H with -#(!) > 0 apply to L with -&(!) > 0


Equilibrium Application Strategies

��

xH (θ) xL(θ)

0 θθ0

nθ ��

xH (θ) xL(θ)

0 θH θθ0

nθ

nγ θ_

Figure: In the left panels, (p∗H , p∗L) = (0.787qH , 0.573qL) with qH − p∗H = qL − p∗L ;

in the right panels, (p∗H , p∗L) = (0.666qH , 0.533qL) with qH − p∗H > qL − p∗L .


Equilibrium Acceptance Rates

��

bH (θ) bL(θ)

0 θθ0

1

��

bH (θ) bL(θ)

0 θH θθ0

qL-pLqH-pH

1




Consumers’ Expected Utilities under Equilibrium

��

U(θ) U(0)-θ

0 θθ0

qH-pH

��

U(θ) U(0)-θ

0 θH θθ0

qL-pL

qH-pH




Consumer to Service Provider Ratio

��

n=0.5 n=1 n=2

pH*

p L*


Fraction of High-Quality Service Providers

��

γ=0.1 γ=0.5 γ=0.9

pH*

p L*


Range of Consumer Serving Costs

��

θ=0.1 θ=0.2 θ=0.4

pH*

p L*


Platform Commission

��

δ=0 δ=0.1 δ=0.5

pH*

p L*


UNILATERAL RATINGS


Consumers’ Problem

Under unilateral ratings, service providers cannot discern low-costconsumers from those with high costs, so they will randomly choose aconsumer given multiple consumers’ applications.

Queue length Xj ≡ NAj , where Aj is a consumer’s applicationprobability. Normalization condition: γXH + (1− γ)XL = n.

Acceptance rate:

Bj = limN→∞

N−1∑i=0

(N − 1

i

)Aij (1− Aj)

N−1−i 1

i + 1=

1− e−Xj

Xj.

A consumer’s maximum expected utility:

U = (qH − pH)1− e−XH

XH= (qL − pL)

1− e−XL

XL.


Service Providers’ Problem

Consider an individual service provider of type j , who deviates to postprice p0

j .

As M →∞, this deviation imposes no impact on U.

Correspondingly, his acceptance rate:

B0j = min

{U

qj − p0j

, 1

}.

The service provider’s profit function:

Π0j (p0

j ; pH , pL) =

[(1− δ)p0

j −θ̄

2g(qj)

]X 0j B

0j ,

where X 0j is the corresponding queue length given B0

j .


Equilibrium

Theorem

Under unilateral ratings, there exists a pure strategy Nash equilibrium(p∗∗H , p

∗∗L ). In the case that g(q) = 1 or g(q) = q, we have that

qH − p∗∗H > qL − p∗∗L .


Comparison of Equilibrium Prices

��

bilateral ratings unilateral ratings

g (qH ) θ_

1-δqH-(qL- g (qL ) θ

_

1-δ) qH

g (qL ) θ_

1-δ

qL

pH*

p L*

Why are equilibrium prices lower under unilateral ratings?

Cost-based market segmentation softens competition.


Comparison of Consumer Surplus

��


0 θθ0

qH* -pH

*

U

Qualitatively similar findings for all parameter settings in comparativestatics studies.


Comparison of Welfare Breakdown

��


high-quality serviceproviders' total profit

low-quality serviceproviders' total profit

platform's profit consumer surplus social welfare


CONCLUSION


Conclusion

Higher prices: Compared with unilateral ratings, bilateral ratingsmay lead to higher prices, and thus lower consumer surplus, due tosoftened competition by market segmentation.

Cost-based market segmentation: consumers with good ratingsapply to only high-quality service providers, and expect a higherutility; while consumers with bad ratings apply to both high-qualityand low-quality service providers, and expect a lower utility.

Higher commission fee from the platform may lower market prices.


Thank You!


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