Pay-What-You-Want in Competition
Margaret Samahita
Department of Economics
Lund University
7 September 2015
Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
PWYW Examples
M. Samahita, Lund University
PWYW Examples
I
Cafes and restaurants: Der Wiener Deewan, Lentil As
Anything, Soul Kitchen, Panera, Terra Bite Lounge
I
Online products: Humble Bundle, Storybundle, Magnatune,
music (eg Amanda Palmer)
I
Travel industry: Museums, Das Park Hotel, Ibis Hotels,
Munster Zoo, “free” walking tours
I
Entertainment industry: Dallas theatre, football clubs (eg
Bath City, Frome Town)
I
Other services: Urban Canine, Wundercar, Activehours,
Google Answers, tipping
I
...
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Questions
PWYW popular in certain industries, and not others.
1. How can PWYW exist?
1.1 Why do sellers adopt PWYW despite the possibility of getting
no revenue?
1.2 Why do customers pay a positive amount without having to do
so?
2. Why is PWYW still not adopted in many other sectors?
M. Samahita, Lund University
Why do sellers adopt PWYW despite the possibility of getting no revenue?
I
Field experiments: prices paid significantly > 0, can lead to
an increase in revenues (Kim et al, 2009)
I
Kish restaurant: PWYW increases customers in the long run
(Kim et al, 2010)
I
Magnatune: consumers do pay voluntarily, even more than
the minimum and recommended amounts (Regner and Barria,
2009)
I
Wiener Deewan: increased customers in the long run though
reduced price, overall increase in revenue (Riener and Traxler,
2012)
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Why do customers pay a positive amount without having to do so?
I
self-image (Gneezy et al, 2012; Jang and Chu, 2012; Kahsay
and Samahita, 2015)
I
social norms (Isaac et al, 2015; Fernandez and Nahata, 2009;
Regner, 2015; Riener and Traxler, 2012)
I
fairness/inequity aversion (Jang and Chu, 2012; Kim et al,
2009; Schmidt et al, 2014)
I
altruism (Schmidt et al, 2014)
I
reciprocity (Regner and Barria, 2009; Regner, 2015)
I
selfish and forward-looking customers (Mak et al, 2015;
Schmidt et al, 2014)
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Why is PWYW still not adopted in many other sectors?
Schmidt et al (2014): lab experiment
I
PWYW viable as monopolist, but less successful in
competition.
I
A significant proportion of buyers prefer FP.
I
PWYW prices are lower compared to PWYW monopolist.
I
Facing PWYW competitor, choosing PWYW is preferred. But
(PWYW,PWYW) is less profitable than (FP,FP).
Chen et al (2009): theoretical model
I
PWYW helps moderate price competition.
I
(PWYW,PWYW) with λ ≥ λ∗ .
I
(FP,FP) with λ < λ∗ .
I
λ∗ ↓ with lower differentiation (lower transport cost).
M. Samahita, Lund University
Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
Utility
I
Simple linear model of consumer utility with surplus-sharing
(see eg Cui et al (2007), Chen et al (2009) and Greiff et al
(2014)).
I
Consumer utility:
Ui = ui − p
I
where ui ∼ U(0, kc), c > 0, k > 1.
Under PWYW
I
I
Free-riders: 0 < θ ≤ 1, zero payment.
Fair buyers: 1 − θ, buy only if ui ≥ c and share λ of surplus,
0 < λ ≤ 1. PWYW payment deterministic:
pi = c + λ(ui − c).
I
λ and θ market parameters, vary by industry or country.
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Monopoly
c(k−1)2
4k
I
πFP =
I
πPWYW =
(1−θ)λc(k−1)2
2k
− θc
Proposition 1
The monopolist will only choose PWYW when
λ > λ̂ =
(k − 1)2 + 4θk
,
2(1 − θ)(k − 1)2
which increases with θ and decreases with k.
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Monopoly
1
λ̂(θ)
0.8 > πFP
> 0, < πFP
0.6
λ
<0
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
θ
Figure 1: PWYW profits, k = 5
With a λ = 1/2 norm, PWYW profit never exceeds FP profit.
M. Samahita, Lund University
Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
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Competition with Homogeneous Products
PWYW
A.1
FP
B.1
PWYW
(PWYW,PWYW)
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B.2
FP
(PWYW,FP)
PWYW
(FP,PWYW)
FP
(FP,FP)
Consumer Behaviour at End Nodes
I
(PWYW,PWYW): buyers randomize, sellers split PWYW profit
πA = πB =
I
(1 − θ)λc(k − 1)2 θc
−
4k
2
(FP,FP): buyers go to the cheaper seller, randomize otherwise
Bertrand outcome: πA = πB = 0
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Consumer Behaviour at End Nodes
I
(PWYW,FP) or (FP,PWYW):
I
I
Free-riders always take the good from the PWYW seller
Fair buyers choose the cheaper of: fixed price p OR PWYW
price pi
no purchase
PWYW , pay pi FP, pay p
c
0
πPWYW = (1 − θ)
M. Samahita, Lund University
λc(k − 1)2
− θc
8k
p
up
πFP = (1 − θ)
ui
kc
λc(k − 1)2
4k
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
FP
2
(1−θ)λc(k−1)
4k
(1−θ)λc(k−1)2
−
8k
θc
(0)
(0)
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
FP
2
(1−θ)λc(k−1)
4k
(1−θ)λc(k−1)2
−
8k
θc
(0)
(0)
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 ⇐⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
FP
2
(1−θ)λc(k−1)
4k
(1−θ)λc(k−1)2
−
8k
θc
(0)
(0)
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 ⇐⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
FP
2
(1−θ)λc(k−1)
4k
(1−θ)λc(k−1)2
−
8k
θc
(0)
(0)
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
FP
2
(1−θ)λc(k−1)
4k
(1−θ)λc(k−1)2
−
8k
θc
(0)
(0)
Profits at End Nodes
λ < λ∗ ⇐⇒
(1−θ)λc(k−1)2
8k
− θc < 0
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
−
8k
FP
θc
(0)
(0)
Profits at End Nodes
λ < λ∗ ⇐⇒
(1−θ)λc(k−1)2
8k
− θc < 0
A.1
PWYW
B.1
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
4k
−
θc
2
−
θc
2
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FP
FP
(1−θ)λc(k−1)2
− θc
8k
(1−θ)λc(k−1)2
4k
B.2
PWYW
(1−θ)λc(k−1)2
4k
(1−θ)λc(k−1)2
−
8k
FP
θc
(0)
(0)
Equilibrium Outcomes
Proposition 2
When two competing sellers choose pricing schemes sequentially
and then enter into a simultaneous price competition, the subgame
perfect equilibrium is either separating or FP-pooling.
Specifically,
i when λ > λ∗ , the first mover chooses FP, and the second mover
chooses PWYW,
ii when λ < λ∗ , the first mover chooses FP, and the second mover
chooses FP,
iii when λ = λ∗ , the first mover chooses FP, and the second mover
randomizes between PWYW and FP,
where λ∗ =
k.
8θk
(1−θ)(k−1)2
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which increases with θ and decreases with
Equilibrium Outcomes
1
I
PWYW used by
second-mover to avoid
Bertrand competition.
I
Anticipated by first-mover,
who chooses FP.
I
First-mover advantage:
PWYW profit lower than FP
profit and as monopolist.
I
No (PWYW,PWYW)
equilibrium.
0.8
λ∗ (θ)
(FP,FP)
λ
0.6
0.4
(FP,PWYW)
0.2
0
0
0.2
0.4
0.6
0.8
1
θ
Figure 2: SPNE outcomes, k = 5
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Product Differentiation
Assumptions
I
Hotelling linear city of length 1.
I
Transport cost t > 0.
I
ui = v = kc
2
be covered.
I
θ = 0.
I
Consumer i located at xi has utility Ui = v − tx − pL if he
buys from Seller L located at 0, and Ui = v − t(1 − x) − pR
from Seller R located at 1. If either chose PWYW,
pi = c + λ(v − c) as before.
I
Sequential choice of pricing schemes, then (simultaneous)
choice of fixed price(s).
I
Indifferent seller chooses FP.
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∀i, k > max{2 +
3t
c ,2
+
t
c(1−λ) }
for market to
Consumer Behaviour at End Nodes
I
(FP,FP): indifferent consumer at x = 1/2,
πL = πR =
I
(PWYW,PWYW): indifferent consumer at x = 1/2,
πL = πR =
I
t
2
λ(v − c)
2
Seller L chooses PWYW, Seller R chooses FP: indifferent
consumer at x = 34 − λ(v4t−c) ,
πPWYW =
3λ(v − c) λ2 (v − c)2
−
4
4t
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πFP =
((t + λ(v − c))2
8t
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
3λ(v −c)
λ2 (v −c)2
−
4
4t
FP
t
2
t
2
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
3λ(v −c)
λ2 (v −c)2
−
4
4t
FP
t
2
t
2
Profits at End Nodes
3λ(v −c)
4
−
λ2 (v −c)2
4t
>
t
2
⇐⇒ λ ∈
t
2t
v −c , v −c
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
3λ(v −c)
λ2 (v −c)2
−
4
4t
FP
t
2
t
2
Profits at End Nodes
λ∈
t
2t
v −c , v −c
=⇒
(t+λ(v −c))2
8t
>
3λ(v −c)
4
−
λ2 (v −c)2
4t
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
3λ(v −c)
λ2 (v −c)2
−
4
4t
FP
t
2
t
2
Profits at End Nodes
(1−θ)λc(k−1)2
8k
− θc > 0 =⇒ λ >
8θk
(1−θ)(k−1)2
:= λ∗
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
3λ(v −c)
λ2 (v −c)2
−
4
4t
FP
t
2
t
2
Profits at End Nodes
λ 6∈
2t
t
v −c , v −c
⇐⇒
3λ(v −c)
4
−
λ2 (v −c)2
4t
<
t
2
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
λ2 (v −c)2
3λ(v −c)
−
4
4t
FP
t
2
t
2
Profits at End Nodes
λ 6∈
2t
t
v −c , v −c
⇐⇒
3λ(v −c)
4
−
λ2 (v −c)2
4t
<
t
2
A.1
PWYW
PWYW
λ(v −c)
2 λ(v −c)
2
B.1
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FP
FP
2
2
3λ(v −c)
− λ (v4t−c)
4
(t+λ(v −c))2
8t
PWYW
2
B.2
(t+λ(v −c))
8t
λ2 (v −c)2
3λ(v −c)
−
4
4t
FP
t
2
t
2
Equilibrium Outcomes
Proposition 3
When two competing sellers of differentiated products choose
pricing schemes sequentially and then enter into a simultaneous
price competition, the subgame perfect equilibrium is either
separating or FP-pooling. Specifically,
i when
4t
2t
<λ<
,
(k − 2)c
(k − 2)c
the first mover chooses FP and the second mover chooses
PWYW,
ii otherwise, both sellers choose FP.
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Equilibrium Outcomes
(FP,FP)
0
(FP,PWYW)
2t
(k−2)c
(FP,FP)
4t
(k−2)c
1
λ
Figure 3: SPNE outcomes
I
Again, first-mover chooses FP
I
Low λ: PWYW attractive to consumers but low profit for seller
I
High λ: PWYW highly profitable but low demand
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Increase in Product Differentiation
Corollary
i
h
λ(k−2)c)
4t
Given λ > (k−2)c
,
the
, when t increases to t 0 ∈ λ(k−2)c
4
2
FP-pooling equilibrium becomes separating.
I
Low t: low PWYW demand as FP competitor can undercut
PWYW “price”.
I
As t increases, location of indifferent consumer increases and
PWYW demand increases up till x = 3/4.
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Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
Welfare - Monopoly
Proposition 4
In an economy with a monopolist seller, PWYW will only be
2
preferred by both the seller and buyers if θ ≤ (k−1)
and
4
λ̂ ≤ λ ≤ λ̄, where λ̂ =
(k−1)2 +4θk
2(1−θ)(k−1)2
and λ̄ =
(k−1)2 (3−4θ)+4k 2 θ
.
4(1−θ)(k−1)2
I
Low θ: minimise dead-weight loss
I
Intermediate λ: high enough for seller but low enough for
buyers
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Welfare - Competition with Homogeneous Products
Proposition 5
In an economy with two competing sellers selling a homogeneous
product, whenever the separating equilibrium obtains, it will never
be preferred by buyers.
I
Separating equilibrium preferred by free-riders but not fair
buyers
I
PWYW presence implies not enough free-riders and too high
surplus-sharing
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Welfare - Competition with Differentiated Products
Proposition 6
In an economy with two competing sellers selling a differentiated
product, whenever the separating equilibrium obtains, it will never
be preferred by buyers.
I
Separating equilibrium preferred if low surplus-sharing
I
Incompatible with seller’s preference
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Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
Empirical Observations
I
77 empirical examples from PWYW Google news alerts
Mar-14 to Apr-15 and academic literature.
I
Classify by SIC Division: “E” Transportation, Communications,
Electric, Gas, And Sanitary Services, “G” Retail Trade, “H”
Finance, Insurance, And Real Estate, “I” Services.
I
Market structure: monopoly if no other seller in the same city,
else competition
I
Geographical PD: physical location
I
PD in characteristics: if no close substitute
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0
10
20
30
40
50
Market Structure
E
G
Monopoly
I
I
I
I
H
I
Competition
Retail (food, online products) and services (hotel and tourist
attractions)
Competition
14% have charity component to increase λ
No PWYW-dominated industry, but entry behaviour consistent
with model predictions
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0
10
20
30
40
50
Geographical Product Differentiation
E
G
GeoPD
H
I
NoGeoPD
I
Physical store + lower social distance translate to high t and
λ, a profitable combination
I
Online stores have low c, hence more likely for separating
equilibrium to obtain
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0
10
20
30
40
50
Differentiation in Product Characteristics
E
G
ProductPD
I
H
I
NoProductPD
Product differentiation: almost all sellers in retail and services
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Outline
1 Introduction
PWYW Examples
Previous Literature
2 The Model
Specifications
Monopoly
3 Competition
Homogeneous Products
Product Differentiation
4 Welfare
5 Empirical Observations
6 Summary
M. Samahita, Lund University
Summary
I
PWYW profitability depends not only on consumers’ social
preferences, but also on market structure, product
characteristics and sellers’ strategies
I
No equilibrium where PWYW dominates
I
Given sufficiently high surplus-sharing and product
differentiation, PWYW chosen when facing FP seller to avoid
Bertrand competition
I
If surplus-sharing too low, FP dominates
I
Consistent with well known examples of PWYW in the market
Thank you!
M. Samahita, Lund University