Supply chain management in the presence of strategic consumers and consumption externalities

NORTHWESTERN UNIVERSITY
SUPPLY CHAIN MANAGEMENT IN THE PRESENCE OF STRATEGIC
CONSUMERS AND CONSUMPTION EXTERNALITIES
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
Field of Industrial Engineering and Management Sciences
By
KENAN AR
˙
IFO
˘
GLU
EVANSTON, ILLINOIS
August 2012
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c
 Copyright by KENAN AR
˙
IFO
˘
GLU 2012
All Rights Reserved
3
Abstract
SUPPLY CHAIN MANAGEMENT IN THE PRESENCE OF STRATEGIC CONSUMERS AND
CONSUMPTION EXTERNALITIES
KENAN AR
˙
IFO
˘
GLU
In this dissertation, I study the management of supply chains in which consumers’ utilities from the
product depend on the total consumption (consumption externalities) and all parties involved, consumers
as well, maximize their own well-being (strategic consumers). I consider two practical motivations:
vaccine for seasonal influenza (flu) epidemic and high-fashion luxury goods.
In Chapter 2, I study the impact of yield uncertainty (supply side) and self-interested consumers
(demand side) on the inefficiency in the influenza vaccine supply chain. Previous economic studies,
focusing on demand side, find that the equilibrium demand is always less than the socially optimal
demand since self-interested individuals do not internalize the social benefit of protecting others via
reduced infectiousness (positive externality). In contrast, I show that the equilibrium demand can be
greater than the socially optimal demand after accounting for the limited supply due to yield uncertainty
and manufacturer’s incentives. The main driver for this result is a second (negative) externality: self-
interested individuals ignore that vaccinating people with high infection costs is more beneficial for

the society when supply is limited. I show that the extent of the negative externality can be reduced
through more efficient and less uncertain allocation mechanisms. In order to investigate the relative
effectiveness of government interventions on supply and demand sides under various demand and supply
4
characteristics, I construct two partially centralized scenarios, where the social planner (government)
intervenes either on the demand side or the supply side but not both, and conduct an extensive numerical
analysis.
In Chapter 3, I develop a mechanism which coordinates a supply chain with consumption exter-
nalities and a profit-maximizing manufacturer having uncertain production process in the presence of
rational consumers. This mechanism includes tax/subsidy payments on the demand side (individual con-
sumers) and a transfer payment on the supply side (manufacturer). I show that, under the mechanism,
the manufacturer is ex ante better off; moreover, expected total utility of all individuals are higher. I also
show that the mechanism allows arbitrary division of ex ante total social welfare between individuals and
the manufacturer.
Chapter 4 develops an analytical model to study the impact of snobbish (exclusivity-seeking) con-
sumer behavior on a firm’s price and quantity decisions. I consider a profit-maximizing monopoly firm
selling a product over two periods to two segments of consumers (with high and low valuation of the
product), who are forward-looking and snobbish, i.e., their valuation of the product decreases as more
people in the population consume it. This modeling framework enables me to explain the heterogeneity
in pricing of snob appeal products observed in practice. Specifically, I find that markdown pricing is op-
timal when the fraction of high-value consumers is small whereas uniform pricing is optimal when this
fraction is large. Thus, snobbish consumer behavior provides another motivation for markdown pricing.
When selling to snobbish consumers, inter-temporal price discrimination increases product exclusivity
and hence consumers’ willingness to pay, in addition to the usual effect of attracting consumers with
different valuations. Similar to normal products, I find that advance purchase discounts are optimal only
when consumers do not know their true valuations in the first period. However, I show that snobbish
consumer behavior coupled with uncertain valuations may lead to discounts in advance. I use this mod-
eling framework to formally distinguish between scarcity and exclusivity, where the former is defined
with respect to the demand whereas the latter is defined with respect to the entire population. I find that
5

snobbish consumer behavior leads to scarcity, but not necessarily to exclusivity, i.e., the product may be
exclusive even when consumers are not snobbish. Finally, contrary to intuition, I find that the product
may become more exclusive when the price is marked down and hence price markdowns need not always
be associated with excess inventory when selling to snobbish consumers.
6
Acknowledgements
This dissertation would not have been possible without the guidance of my committee members,
help from friends, and support from my family.
I would like to express my deepest gratitude to my principal advisor, Prof. Seyed Iravani, for his
guidance, caring, and providing me with an excellent free research atmosphere. I am indebted to my
second advisor, Prof. Sarang Deo. I thank him for many stimulating academic discussions, his dedicated
advising, his work ethic, and his incredible involvement, support and encouragement. I learned a lot
from both of my advisors.
I am very grateful to Prof. Izak Duenyas for his guidance and support during my research assist-
antship at the University of Michigan. He was a great resource for me. I enjoyed working with him
and engaging in academic discussions. I thank my committee member Prof. Diego Klabjan for his
thought-provoking questions and suggestions.
I thank Prof. Martin Larivieri for always being there to discuss research problems. His suggestions
greatly improved this dissertation. I thank Prof. Barıs¸ Ata for his mentorship.
I have been very fortunate to know many people during my doctoral study at Northwestern Univer-
sity. I am thankful to all of my professors, classmates, and officemates. My special thanks go to Linlin,
Luis, Mustafa, Neda, and Yan. I have benefited a lot from my conversations with them. I also would like
to thank Ahmet, Betul, Can, G
¨
okhan, G
¨
urkan, Kezban, Koray, Muzaffer, and Yasin. They were a constant
source of encouragement and support; it would have been very boring without their companionship.
7
Last, but definitely not the least, I am immensely grateful to my family, especially to my parents. It

was their unconditional love, care, and encouragement which made this dissertation possible. Without
their support, I do not think that I could overcome the difficulties during these years.
8
Dedication
To my parents,
Ali and Radet Arifo
˘
glu,
who made all of this possible,
for their love and continuous support.
9
Contents
Abstract 3
Acknowledgements 6
Dedication 8
List of Tables 11
List of Figures 12
Chapter 1. Introduction 14
Chapter 2. Consumption Externality and Yield Uncertainty in the Influenza Vaccine Supply Chain:
Interventions in Demand and Supply Sides 19
2.1. Introduction 19
2.2. Literature Review 22
2.3. Model and Assumptions 24
2.4. Equilibrium in the Decentralized System 28
2.5. Optimal Solution of the Centralized System 33
2.6. Government Interventions 39
2.7. Deterministic Yield 43
2.8. Numerical Study 44
2.9. Conclusion and Future Research 50
2.A. Appendix for Chapter 2 51

10
Chapter 3. Coordinating Supply Chains with Uncertain Yield and Consumption Externalities 79
3.1. Introduction 79
3.2. Related Literature 81
3.3. Model Fundamentals 83
3.4. Social Optimum 86
3.5. Supply Chain Inefficiency and Coordination 88
3.6. Conclusion 97
3.A. Appendix for Chapter 3 99
Chapter 4. Pricing and Strategic Rationing When Selling to Snobbish Consumers 106
4.1. Introduction 106
4.2. Review of the Related Literature 110
4.3. Model Description 112
4.4. Capacity under Different Pricing Policies 114
4.5. Optimal Selling Strategy with Deterministic Consumer Valuations 122
4.6. Extensions 129
4.7. Conclusion and Future Research 138
4.A. Appendix for Chapter 4 140
Chapter 5. Conclusion and Future Research 162
5.1. Summary 162
5.2. Future research 165
Bibliography 167
11
List of Tables
2.1 Characterization of four systems analyzed 40
2.2 Values of input parameters 46
4.1 Equilibrium capacity with potentially-optimal APD when the population is
homogeneous and consumer valuations are uncertain. 117
4.2 Equilibrium price, capacity and demand with potentially-optimal UP when the
population is homogenous and consumer valuations are uncertain. 119

4.3 Equilibrium capacity with potentially-optimal MP when the population is homogeneous
and consumer valuations are uncertain. 121
4.4 Equilibrium price, capacity and demand with potentially-optimal UP when the
population is heterogeneous and consumer valuations are deterministic. 132
4.5 Equilibrium price, capacity and demand with potentially-optimal MP when the
population is heterogeneous and consumer valuations are deterministic. 133
4.6 Equilibrium price, capacity and demand with potentially-optimal UP when the
population is homogenous and consumer valuations are deterministic. 150
4.7 Equilibrium capacity with potentially-optimal MP when the population is homogenous
and consumer valuations are deterministic. 150
12
List of Figures
2.1 Demand in the decentralized and centralized systems 31
2.2 Marginal social benefit when social planner decides the demand, where B (δ) is given
by (2.14) 39
2.3 Value of centralized solution, and supply-side and demand-side interventions for
w/c = 2, c = 3, θ = 10 and β = 0.25
¯
δ 46
2.4 Sensitivity analysis of Availability and Negative Externality Effects when R
0
= 3. The
socially optimal β in each case is pointed by an arrow. 49
2.5 (a) Ex post demand in the decentralized equilibrium and social optimum; (b) The
probability density function (PDF) and cumulative distribution function (CDF) of yield 53
2.6 (a) Ex post demand in the decentralized equilibrium and social optimum; (b) The
probability density function (PDF) and cumulative distribution function (CDF) of yield 54
3.1 The additional gain/loss from vaccination under the mechanism (t
nv
(Q

r
) − t
v
(Q
r
)) 94
3.2 Transfer payment from the government to the manufacturer (T (Q
r
)). 97
4.1 Firm’s selling strategy when consumer valuations are deterministic, i.e., α = 1
and β = 0. For a fixed v
H
, the plane (λ, θ) is divided into four (I-IV) regions.
The
˜
θ functions defining the boundary of regions are given by (4.30)-(4.32).
123
13
4.2 Firm’s capacity and the discount rate as a function of sensitivity to consumption (λ)
when consumer valuations are deterministic, and v
H
= 15, v
L
= 5, c = 1, θ
∗
 0.286
and N = 1000. 127
4.3 Firm’s optimal selling strategy when N = 1000, v
H
= 15, v

L
= 5 and c = 1. 136
14
CHAPTER 1
Introduction
According to Global Supply Chain Forum,
Supply chain management (SCM) is the integration of key business processes across the
supply chain for the purpose of creating value for customers and stakeholders [Cooper
et al., 1997].
In the last 30 years, SCM has gotten a lot of scholarly attention. Researchers in operations management
/research studied various aspects of SCM, i.e., number and location of facilities in a supply chain, amount
of capacity at each facility, allocation of facilities to market locations, inventory control, coordination and
information sharing between the parties in a supply chain, etc.
Chopra and Meindl [2004, pg. 31] consider “understanding the customer” as an essential part of
SCM. The way consumers think and their motivations for consumption affect both marketing and supply
chain strategies (i.e., operations, distribution and service) of a firm. Despite its importance, research
modeling the effect of consumer behavior on supply chain strategies has recently started. Several papers
in operations management [Dana and Petruzzi, 2001; Su and Zhang, 2008; Liu and van Ryzin, 2008;
Cachon and Swinney, 2009] study forward-looking (strategic) consumer behavior. These papers assume
that consumers are no longer myopic and choose the time of their purchase so as to maximize their utility.
They show that strategic consumer behavior affects the pricing policy and capacity decision of a firm.
For example, a firm selling to strategic consumers should set a lower capacity when the price is marked
down over time since this discourages strategic consumers from waiting for lower prices [Su and Zhang,
2008; Liu and van Ryzin, 2008].
15
A consumer’s purchasing behavior is not independent from that of other consumers. For example,
if a consumer decide to buy the product, she decreases the product availability for all other consumers,
as a result, it imposes negative consumption externality among consumers who are willing to purchase
the product. This, in turn, discourages the consumers with low valuations from buying which results
in lower aggregate demand. Operations management papers modeling strategic consumer behavior also

consider the dependence between product availability and consumers’ purchasing decisions (see Shen
and Su [2007] and Aviv et al. [2009] for an overview of these papers).
However, consumption externalities affect the purchasing behavior of consumers not only through
product availability. In fact, consumers value certain products based on the total consumption. For ex-
ample, if too many people are vaccinated against an infectious disease, probability of infection is very
low for each unvaccinated individual, so is the value of the vaccine. Similarly, a BMW on every drive-
way may dilute the value of the car to consumers [Amaldoss and Jain, 2005a]. Except two recent studies
[Agrawal et al., 2011; Tereya
˘
go
˘
glu and Veeraraghavan, 2012], the dependence of consumer valuations on
the total consumption is not studied in operations literature. Both Agrawal et al. [2011] and Tereya
˘
go
˘
glu
and Veeraraghavan [2012] assume that consumers are exclusivity-seeking (snobbish), i.e., the product is
less valuable if too many people purchase it. Agrawal et al. [2011] analyze product design and introduc-
tion decisions of a firm selling a durable good to snobbish consumers. They show that firms selling to
snobbish consumers should design products that undergo slow value erosion, and should introduce them
at high-price and low-volume. Tereya
˘
go
˘
glu and Veeraraghavan [2012] analyze the pricing and produc-
tion decisions of a firm selling to a heterogeneous market which also includes snobbish consumers. They
show that, depending on the market composition and consumers’ sensitivity to consumption, the firm
may charge a higher price and set a lower capacity when selling to snobbish consumers.
Certainly, a model ignoring strategic consumer behavior and consumption externalities cannot ac-

curately represent the supply chain of certain products. The solution of such a model may exacerbate
16
the total supply chain inefficiency. Thus, in this research, we study the supply chains with strategic con-
sumer behavior and consumption externalities. Our research is particularly motivated by the vaccine for
seasonal influenza (flu) epidemic and luxury goods.
In Chapter 2, we study the influenza (flu) vaccine supply chain in the USA. The influenza vaccine
in the USA is produced by private companies through a complex and unreliable production process and
consumers make their vaccination decisions in a rational and self-interested way [Pauly, 2005; Vietri
et al., 2008]. The supply chain of vaccines, especially that of influenza vaccine, has long been studied
by researchers in health economics (i.e., Brito et al. [1991]), epidemiology (i.e., Bauch and Earn [2004];
Reluga et al. [2006]; Galvani et al. [2007]) and operations management (i.e., Chick et al. [2008]; Deo and
Corbett [2009]). Papers in health economics and epidemiology literatures focus only on the rational de-
cision making by consumers and assume that the vaccine supply is unlimited whereas those in operations
management literature study only the supply side and ignore the rational decision making by consumers.
However, we consider both supply and demand sides and show that the interaction between them leads
to novel insights. For example, Brito et al. [1991] find that when the vaccine supply is unlimited, the
supply chain inefficiency is due to the positive externality, i.e., each consumer considers only direct ben-
efits from vaccination but ignore the social benefits due to protecting others via reduced infectiousness,
and hence the demand is lower in equilibrium than in the socially-optimal solution. In contrast, we show
that when supply is endogenized, the supply chain inefficiency may be due to the negative externality,
i.e., when the vaccine supply is limited, each consumer searching for the vaccine reduces the vaccine
availability for other consumers, which results in equilibrium demand being higher than socially-optimal
demand. Problems related to flu vaccine supply chain in the recent past have generated a lot of public
as well as scholarly reactions advocating a need for a more active role by the government [Kilbourne,
1991; Harris, 2006; Hinman, 2005a]. However, there is considerable debate about the exact nature of this
intervention. Opinions range from interventions focusing solely on the demand side (to induce demand)
such as increased insurance coverage, improving accessibility and public awareness campaigns [Institute
17
of Medicine, 2004; Hinman, 2005b], to those focusing solely on the supply-side (to ensure more sup-
ply) such as subsidizing the manufacturers and even owning production facilities [Grady, 2004; Hinman

et al., 2005]. To address this policy debate, in Chapter 2, we also analyze the relative effectiveness of
government interventions in only one (demand or supply) side of the supply chain.
In Chapter 3, motivated by flu vaccine supply chain, we design a mechanism which eliminates the
entire inefficiency in a supply chain with consumption externalities and a profit-maximizing manufac-
turer having uncertain production yield. This mechanism aligns consumers’ incentives with social op-
timum through tax and subsidies on the demand side. To eliminate the inefficiency due to negative
externality, the mechanism curbs the demand by taxing/subsidizing vaccinated/unvaccinated consumers
for low realizations of production quantity. On the other hand, for high realization of production quan-
tity, it taxes/subsidizes unvaccinated/vaccinated consumers to induce the demand and to decrease the
inefficiency due to positive externality. On the supply side, our mechanism requires a transfer payment
between the manufacturer and social planner. Through this transfer payment, the social planner shares
the manufacturer’s risk due to uncetain yield.
In Chapter 4, motivated by high-fashion luxury products, we develop a model to study the pricing
policy and capacity decision of a monopolist firm selling a product over two periods to strategic and
snobbish consumers who value a product less as more people consume it. The literature has identi-
fied demand uncertainty [Rodriguez and Locay, 2002; Nocke and Peitz, 2007], risk-averse attitude of
consumers [Liu and van Ryzin, 2008] and uncertain consumer valuations [M
¨
oller and Watanabe, 2010]
as some reasons why firms use inter-temporal pricing (e.g., price markdowns or advance purchase dis-
counts) and why they create scarcity intentionally. We complement the literature by studying the implica-
tions of snobbish consumer behavior on firm’s pricing policy and capacity decision. We show that firms
selling snob-appeal products intentionally create scarcity due to exclusivity-seeking consumer behavior
[Rosenbloom, November 19, 2009]. We also find that the snobbish consumer behavior itself leads to the
optimality of inter-temporal pricing when the number of consumers valuing the product high is low. Due
18
exclusivity-seeking consumer behavior, the firm creates scarcity to charge a higher price which creates
rationing risk. Consumers with high valuations can pay more not to be rationed. Therefore, the firm
sells the product at higher price and only consumers with high valuations purchase. Later, she reduces
the price and satisfy demand coming from consumers with lower valuations. When the number of con-

sumers with high valuations is very large (i.e., the firm has high brand image), the firm does not mark the
price down and always charges a very high uniform price. Consistent with this result, we observe that
brands with high image, e.g., Louis Vuitton and Hermes, never discount [Sherman, July 10, 2009].
Lastly, we summarize our main findings and discuss about the ideas for future research in Chapter 5.
19
CHAPTER 2
Consumption Externality and Yield Uncertainty in the Influenza Vaccine
Supply Chain: Interventions in Demand and Supply Sides
2.1. Introduction
Unlike pediatric vaccines, supply chain for the influenza (flu) vaccine in the U.S. is highly decen-
tralized. Profit maximizing firms decide the production quantity and bring the produced vaccine to the
market while individuals decide whether or not to get vaccinated in a rational and self-interested manner
based on the availability of the vaccine, severity of the infection, and vaccination costs [Vietri et al.,
2008]. The role of the government and its agencies such as the Center for Diseases Control and Pre-
vention (CDC) is limited to deciding the vaccine composition and recommending priority groups for
vaccination [Institute of Medicine, 2004; Government Accountability Office, 2004]. On the supply side,
potentially insufficient incentives of manufacturers together with a long production process (six to eight
months) and the significant uncertainty in the production yield have contributed to shortages in the re-
cent past [Government Accountability Office, 2004]. On the demand side, positive externality effect
associated with vaccination—each vaccinated individual decreases the infection risk of her close con-
tacts but fails to internalize this value while making her own vaccination decision [Brito et al., 1991]—
has arguably contributed to vaccination coverage rates that are lower than the socially desired target rates
[Harper et al., 2005].
20
In this chapter, we develop an integrated model of production (yield) uncertainty and rational
1
con-
sumer behavior, and investigate the interaction between these two potential sources of inefficiency. Mo-
tivated by the current practice, we study a decentralized system where the manufacturer determines the
production quantity and individuals make their vaccination decisions. We consider a single flu season

and a population comprising two priority groups based on the infection disutility of its individuals. First,
given the design of priority groups, the manufacturer decides the production quantity and incurs the re-
lated production cost. A random fraction of this production quantity is realized and brought to the market.
The supply received at the beginning of the flu season is first allocated to the group with higher infection
disutility, and the remaining supply, if any, is then allocated to the group with lower infection disutil-
ity. Then, knowing the design of priority groups and observing the realized production, self-interested
individuals decide whether to spend time and money to search (e.g., physical travel or information col-
lection) for the vaccine. Due to limited supply, individuals that decide to search are not guaranteed to get
the vaccine. Unvaccinated individuals, irrespective of whether they search for the vaccine or not, may be
infected with some probability that depends on the vaccinated fraction of the population. Every infected
individual incurs some infection disutility (e.g., payment for drugs, health care costs, lost wages, death).
Vaccinated individuals become immune against influenza but may incur some vaccination disutility (e.g.,
side effects, vaccine price, administration costs).
We also analyze a benchmark centralized system where a social planner decides the demand and
the production quantity to maximize the total social welfare. We find that the production quantity in
the centralized setting is always greater than that in the decentralized setting in accordance with previous
supply-chain models of yield uncertainty. However, contrary to existing economic models of vaccination,
we find that the expected demand in the decentralized setting can be higher than that in the centralized
setting.
1
We use the term “rational” or “self-interested” interchangeably to refer to an individual that maximizes her own expected net
utility.
21
This result is driven by the negative externality effect—when the vaccine supply is limited, each
individual searching for the vaccine reduces the vaccine availability for some individuals with higher
infection disutility but does not internalize this cost. The negative externality effect causes inefficiency
(i.e., lower social welfare) on the demand side under limited supply for two main reasons: (i) not all
individuals searching for the vaccine can get it and hence wasteful search costs are incurred, and (ii)
those who need vaccine the most (individuals with high infection disutility) may not get it. The first
component is due to the uncertainty/randomness in the vaccine allocation, i.e., if individuals who failed

to get the vaccine knew this a priori, they would not seek vaccination so that the equilibrium demand
will be equal to the available supply. The second component is due to the inefficiency in the allocation of
vaccines, i.e., if the vaccine was allocated to individuals in decreasing order of their infection disutility,
individuals with higher infection disutility would be vaccinated first.
In order to understand the impact of prioritization, we analyze a model with a completely random
allocation mechanism and a single group of individuals. We show that prioritization makes the vaccine
allocation more efficient and less uncertain by increasing the chance of obtaining the vaccine for individ-
uals with high infection disutility. As a result, we find that the negative externality effect is smaller under
the priority scheme with two groups than under a complete random allocation with no priority groups.
Increasing the number of priority groups reduces the negative externality effect further by decreasing the
inefficiency and uncertainty in the allocation mechanism.
In addition, we study how individuals accounting for the limited supply affect the total social welfare.
For this purpose, we define availability effect as the difference in the equilibrium outcomes between the
decentralized system and a reference case, where the fill rate is 1 and where the infection probability is
based on unlimited supply. We find that this availability effect is beneficial to the society when search
costs are high and infection disutilities among individuals are low. In such cases, accounting for limited
availability of vaccines decreases the incentive for individuals with low infection disutility to search for
22
vaccines compared to the reference case, which results in lower wasteful search costs and better vaccine
allocation for individuals with high infection disutility.
We also construct partially centralized models to inform the public policy debate regarding the rela-
tive effectiveness of government intervention on the demand side [Institute of Medicine, 2004; Hinman,
2005b] vs. supply side [Grady, 2004; Hinman et al., 2005]. Under the demand-side intervention, the
manufacturer chooses profit maximizing production quantity but the social planner chooses the demand
to maximize the total social welfare. Under the supply-side intervention, the social planner decides the
welfare maximizing production quantity but the demand is determined by self-interested individuals.
We find that the demand-side intervention in some cases can provide “too much” incentive (expected
marginal benefit) to the manufacturer and results in production quantity that is greater than that in the
centralized solution. Similarly, the production quantity under supply-side intervention can be higher than
that in the social optimum, especially at lower yield realizations, to compensate for the self-interested

behavior of individuals. When a large fraction of the population has high infection disutility, the demand-
side inefficiency due to negative externality effect is high and the manufacturer underproduces due to high
supply risk and lower marginal benefits. In such cases, we find that the social planner should intervene
in the supply side to increase the production levels and consequently decrease the negative externality
effect. On the contrary, when a large fraction of population has low infection disutility and the epidemic
is less infectious, individuals have less willingness to search for the vaccine. In such cases, the social
planner can improve total social welfare more by intervening on the demand side.
2.2. Literature Review
In this section, we outline our contribution to three distinct streams of literature.
23
2.2.1. Operations management literature
Our consumer model contributes to the growing literature on supply-chain management in the presence
of strategic consumer behavior [Dana and Petruzzi, 2001; Su and Zhang, 2008; Cachon and Swinney,
2009]. Most papers in this stream assume that the valuation of the product for rational consumers is
exogenously specified. To our knowledge, ours is among the first papers to consider a supply chain
with consumption externality, i.e., consumers’ valuation for the product is determined as a function
of the fraction of market consuming the product in equilibrium. In a recent paper, Tereya
˘
go
˘
glu and
Veeraraghavan [2012] analyze a model with consumption externality similar to ours. However, ours
differs significantly in various modeling elements such as yield uncertainty, heterogeneity of consumer
valuations, allocation mechanism, and partially centralized scenarios.
Flu vaccine supply chain has drawn considerable attention from OM researchers recently [Wu et al.,
2007; Kornish and Keeney, 2008; Chick et al., 2008; Deo and Corbett, 2009; Cho, 2010]. Deo and
Corbett [2009], using a model of Cournot competition with endogenous entry, show that yield uncer-
tainty can explain the high concentration of the U.S. flu vaccine market. Chick et al. [2008] propose
a cost-sharing contract to eliminate the supply-side inefficiency, i.e., a profit-maximizing manufacturer
produces less vaccine compared to the socially-optimal solution. We complement them by incorporating

rational consumer behavior, examining the interaction between the demand side and supply side, and
deriving relevant policy implications.
2.2.2. Health economics literature
Several papers in health economics analyze the externality arising from vaccination and find that the
demand for vaccines is lower in equilibrium than in the socially-optimal solution [Brito et al., 1991;
Geoffard and Philipson, 1996; Philipson, 2000]. In contrast, we show that when supply is endogenized,
it can result in equilibrium demand that is higher than the socially-optimal demand due to the negative
externality arising from limited and stochastic supply. This effect acts counter to the positive externality
24
effect from herd immunity, which results in lower than socially-optimal demand. For some instances of
yield uncertainty, the latter effect dominates the former effect, thereby resulting in higher demand.
2.2.3. Epidemiology literature
Empirical evidence suggests that the decision to vaccinate is also strongly correlated with the vaccine
effectiveness, flu severity, and vaccine side effects [Chapman and Coups, 1999]. Several studies [Bauch
and Earn, 2004; Reluga et al., 2006; Galvani et al., 2007] combine epidemiologic models and deductive
game-theoretic models to analyze rational vaccination decisions by individuals in the presence of these
factors. These models are also consistent with the health benefit model [Janz and Becker, 1984], which
has been shown to explain vaccination decisions of individuals [Larson et al., 1979]. Given the strong
empirical support, we also adopt a deductive
2
game approach but also incorporate the impact of supply-
side factors such as yield uncertainty, which is missing from the earlier models.
2.3. Model and Assumptions
In this section, we describe various components of our model.
2.3.1. Supply model
Injectable vaccines produced via embryonated chicken eggs still constitute majority (over 97%) of flu
vaccine produced and administered [Danzon et al., 2005; Palese, 2006; Government Accountability Of-
fice, 2008]. An important characteristic of this process is yield uncertainty due to uncertain growth
characteristics of virus strains inside the chicken eggs and the possibility of bacterial contamination. In
accordance with the models proposed in the literature [Palese, 2006; Chick et al., 2008; Deo and Corbett,

2009], we assume that the obtained number of vaccine doses Q
r
is a stochastic proportion of the planned
egg production Q (see Yano and Lee [1995] for models with proportional yield). That is, Q
r
= UQ,
2
For an alternative inductive game formulation, where individuals base their decisions on past experience only, see Breban et al.
[2007].