Young Kwark. Warrington College of Business, University of Florida, 1454 Union Road, Gainesville, FL U.S.A.

Σχετικά έγγραφα
ΗΥ537: Έλεγχος Πόρων και Επίδοση σε Ευρυζωνικά Δίκτυα,

α & β spatial orbitals in

A Class of Orthohomological Triangles

One and two particle density matrices for single determinant HF wavefunctions. (1) = φ 2. )β(1) ( ) ) + β(1)β * β. (1)ρ RHF

Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών. ΗΥ-570: Στατιστική Επεξεργασία Σήµατος. ιδάσκων : Α. Μουχτάρης. εύτερη Σειρά Ασκήσεων.

Constant Elasticity of Substitution in Applied General Equilibrium

Multi-dimensional Central Limit Theorem

Multi-dimensional Central Limit Theorem

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

Every set of first-order formulas is equivalent to an independent set

Supplementary materials for Statistical Estimation and Testing via the Sorted l 1 Norm

Finite Field Problems: Solutions

Variance of Trait in an Inbred Population. Variance of Trait in an Inbred Population

Matrices and Determinants

8.324 Relativistic Quantum Field Theory II

1 Complete Set of Grassmann States

8.1 The Nature of Heteroskedasticity 8.2 Using the Least Squares Estimator 8.3 The Generalized Least Squares Estimator 8.

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

Symplecticity of the Störmer-Verlet algorithm for coupling between the shallow water equations and horizontal vehicle motion

Supporting information for: Functional Mixed Effects Model for Small Area Estimation

C.S. 430 Assignment 6, Sample Solutions

Duals of the QCQP and SDP Sparse SVM. Antoni B. Chan, Nuno Vasconcelos, and Gert R. G. Lanckriet

Phasor Diagram of an RC Circuit V R

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Math221: HW# 1 solutions

Fractional Colorings and Zykov Products of graphs

Notes on the Open Economy

EE512: Error Control Coding

Right Rear Door. Let's now finish the door hinge saga with the right rear door

derivation of the Laplacian from rectangular to spherical coordinates

Generalized Fibonacci-Like Polynomial and its. Determinantal Identities

Srednicki Chapter 55

LECTURE 4 : ARMA PROCESSES

Homework 8 Model Solution Section

2 Composition. Invertible Mappings

Homework 3 Solutions

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

Derivation for Input of Factor Graph Representation

Commutative Monoids in Intuitionistic Fuzzy Sets

CRASH COURSE IN PRECALCULUS

Section 8.3 Trigonometric Equations

CAPM. VaR Value at Risk. VaR. RAROC Risk-Adjusted Return on Capital

Neutralino contributions to Dark Matter, LHC and future Linear Collider searches

35 90% %

Example Sheet 3 Solutions

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών

ΠΤΥΧΙΑΚΗ/ ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Mean-Variance Analysis

Power allocation under per-antenna power constraints in multiuser MIMO systems

c Key words: cultivation of blood, two-sets blood culture, detection rate of germ Vol. 18 No

4.6 Autoregressive Moving Average Model ARMA(1,1)

Bayesian modeling of inseparable space-time variation in disease risk

Solutions to Exercise Sheet 5

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

ΜΕΡΟΣ ΙΙΙ ΜΟΡΙΑΚΟ ΒΑΡΟΣ ΠΟΛΥΜΕΡΩΝ

Derivation of Optical-Bloch Equations

ST5224: Advanced Statistical Theory II

Second Order RLC Filters

On Integrability Conditions of Derivation Equations in a Subspace of Asymmetric Affine Connection Space

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

Generalized Linear Model [GLM]

Μεταπτυχιακή διατριβή. Ανδρέας Παπαευσταθίου

ΕΘΝΙΚΗ ΥΟΛΗ ΔΗΜΟΙΑ ΔΙΟΙΚΗΗ ΙH ΕΚΠΑΙΔΕΤΣΙΚΗ ΕΙΡΑ ΤΜΗΜΑ ΚΟΙΝΩΝΙΚΗΣ ΔΙΟΙΚΗΣΗΣ ΔΙΟΙΚΗΣΗ ΜΟΝΑΔΩΝ ΥΓΕΙΑΣ ΤΕΛΙΚΗ ΕΡΓΑΣΙΑ

Estimators when the Correlation Coefficient. is Negative

Some generalization of Cauchy s and Wilson s functional equations on abelian groups

CS 1675 Introduction to Machine Learning Lecture 7. Density estimation. Milos Hauskrecht 5329 Sennott Square

Inverse trigonometric functions & General Solution of Trigonometric Equations

Generating Set of the Complete Semigroups of Binary Relations

Laplace s Equation in Spherical Polar Coördinates

Forced Pendulum Numerical approach

Reminders: linear functions

Second Order Partial Differential Equations

Example 1: THE ELECTRIC DIPOLE

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Statistical Inference I Locally most powerful tests

k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

SCITECH Volume 13, Issue 2 RESEARCH ORGANISATION Published online: March 29, 2018

Solutions for Mathematical Physics 1 (Dated: April 19, 2015)

Congruence Classes of Invertible Matrices of Order 3 over F 2

Vol. 34 ( 2014 ) No. 4. J. of Math. (PRC) : A : (2014) Frank-Wolfe [7],. Frank-Wolfe, ( ).

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

An Inventory of Continuous Distributions

Section 7.6 Double and Half Angle Formulas

The Pohozaev identity for the fractional Laplacian

Μηχανική Μάθηση Hypothesis Testing

2. THEORY OF EQUATIONS. PREVIOUS EAMCET Bits.

ΜΕΡΟΣ ΙΙI ΜΟΡΙΑΚΟ ΒΑΡΟΣ ΠΟΛΥΜΕΡΩΝ

ΕΘΝΙΚΗ ΣΧΟΛΗ ΗΜΟΣΙΑΣ ΙΟΙΚΗΣΗΣ

Analytical Expression for Hessian

Pg The perimeter is P = 3x The area of a triangle is. where b is the base, h is the height. In our case b = x, then the area is

Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee

8. ΕΠΕΞΕΡΓΑΣΊΑ ΣΗΜΆΤΩΝ. ICA: συναρτήσεις κόστους & εφαρμογές

HIV HIV HIV HIV AIDS 3 :.1 /-,**1 +332

Problem Set 3: Solutions

TMA4115 Matematikk 3

Transcript:

ESEC TICE PTFOM O WOESE? STTEGIC TOO FO ONINE ETIES TO ENEFIT FOM TI-PTY INFOMTION Young Kark Warrngton College of usness, Unversty of Florda, 1454 Unon oad, Ganesvlle, F 3611 U.S.. {young.kark@arrngton.ufl.edu} Janqng Chen and Srnvasan aghunathan Jndal School of Management, Unversty of Teas at allas, 800 West Cambell oad, chardson, TX 75080 U.S.. {chenjq@utdallas.edu} {sraghu@utdallas.edu} end ervaton of Condtonal Eectaton of Msft Proof. Cumulatve densty functon of s, condtonal on the consumer s true degree of msft λ beng z, can be formulated as P(s # y λ z (1 y (y z, here (@ s the eavsde ste functon that evaluates to zero f the argument s negatve, and to one otherse. The corresondng robablty densty functon s P(s y λ z (1 δ(y z, here δ( s the rac delta dstrbuton that satsfes Usng the ayes a, δ ( d 0 for 0 1 and δ ( for 0 ( λ P z s y ( λ ( λ Ps ( y Ps y zp z ( 1 δ( y z (44 and the condtonal eectaton s 1 1 E( λ s y λ ( 1 δ( y λ dλ 1 λdλ y y 0 1 0 MIS Quarterly Vol. 41 No. 3 endsetember 017 1

Kark et al. Strategc Tool for Onlne etalers Proof of emma 1 Proof. We denote a 1 (1 γ ( τ, a 1 (1 γ ( τ, b 1( τ α, and c 1( τ. The demand functons n Equaton (8 then can be rertten as: a b c a b c (45 The retaler s otmzaton roblem n stage 1 s characterzed by the frst-order condtons as follos: k ( a b c ( a c b and m (46 The manufacturers otmzaton roblems n stage, gven k and m are characterzed by the frst-order condtons of Equaton (9: (1 k a b c 0 (1 k a b c 0 from hch e can derve the manufacturers otmal retal rces: ab ac 4b c ab ac 4b c (47 Substtutng the retal rces, e can characterze the retaler s equlbrum roft and the manufacturers equlbrum rofts as: [ ( (4 8 ] π k( k b a m a b c a a b c m (4 b c π (1 k b(1 k ba ca m m (4 b c π (1 k b(1 k ca ba m m (4 b c (48 (49 ntcatng the manufacturers artcaton ncentves of sellng on the retaler s latform ( π μ, the retaler sets the otmal k and m by solvng the bndng constrants, π μ, smultaneously: k 1 m (4 b c ( μ μ ba ( a μ ( ca ba μ ( ba ca (4 b c ( a a (4 b c ( a a (50 Substtutng the above otmal retal rces, the commsson rate, and fed fee nto the retaler s roft: MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers b(4 b c ( a a 8b ca a π μ μ (4 b c (51 emma 1 follos by substtutng substtutng a, a, a, b, and c nto the above otmal retal rces, the commsson rate, and fed fee. Smlarly, by a, b, and c nto Equaton (51, the retaler s roft can be derved as (1 ατ τ (1 γ π μ μ τ (1 4 ατ (3 4 ατ (5 Proof of Prooston 1 Proof. We notce ε (3 4 αε (1 γ (1 4 αγε (3 4 αγε (1 γ f and only f ε (3 4 αε (1 γ (1 4 αγε (3 4 αγε hch leads to the condton n Inequalty (15. Substtutng τ γε nto Equaton (5, e have the retaler s roft. (1 γ f and only f ε γ γ αε γ αε 3 3 (1 γ (1 4 αγε γ ε(3 4 αγε (1 3 (3 4 (3 ( 4 hch leads to the condton n Inequalty (16. Proof of Corollary Proof. Throughout the aend, e denote. Consumer surlus ( CS derved from roduct can be formulated as: (1 γ (1 y t 1 γ 0 ε ( ( α 1 ε 1 1 CS y t ddy 0 (1 γ (1 y t ε α 1 1 CS (1 y t ddy ε γ (53 here and are defned as n Equaton (5. The total consumer surlus CS CS CS. y substtutng the otmal retal rces from emma 1, e have MIS Quarterly Vol. 41 No. 3 endsetember 017 3

Kark et al. Strategc Tool for Onlne etalers t t (1 αγε (1 4 αγε (3 4 αγε (6γε 3 γε 6 γ ε (3 4 αγε 6(1 4 αγε (1 γ CS 6 γε (1 4 αγε (3 4 αγε Smlarly, e can derve the socal elfare from roduct as: γ γ (1 (1 y t 1 0 γ ε ( ( α 1 ε 1 1 SW y 0 (1 γ (1 y t ε t ddy α 1 1 SW (1 y t ddy ε (54 The total socal elfare SW SW SW. y substtutng the otmal retal rces from emma 1, e have SW [ t t ] 3 γε ( (1 αγε 6 γε (1 4 αγε When 0, e notce: CS γ εα t αγε γ ε t αγε αγε αγε 3 (1 γ 6 γ ε(1 4 αγε 6 (1 4 6 (1 4 [1 8 (1 ] SW t αγ ε t αγε αγε (1 γ 6 γ ε(1 4 αγε 6 1 8 (1 We can verfy that both are ostve usng a condton that even the consumer th a sgnal ndcatng the largest degree of msft has ncentve to urchase. Proof of Prooston Proof. We notce t 4 αt(1 γ (1 4 αt (3 4 αt f and only f t 4 αt(1 γ (1 4 αt (3 4 αt hch leads to the condton n Inequalty (18. Substtutng τ t nto Equaton (5, e have the retaler s roft. f and only f γ α α 3 3 (1 4 αt t(3 4 αt t (1 [ 3 4 t(3 4 t ] hch leads to the condton n Inequalty (19. 4 MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers Proof of Corollary 4 Proof. Consumer surlus ( CS derved from roduct can be formulated as: 1 y 1 1 y (1 (1 γ y t y ( γ ε 1 1 1 ( ( α y ε CS t dy y t ddy 0 (1 γ (1 y t α y 1 γ CS (1 y t ddy (1 y t y ε y ε dy (55 here y and y are defned as n Equaton (6 and and CS CS CS. y substtutng the otmal retal rces from emma 1, e have are defned as n Equaton (7. The total consumer surlus [ 3 ] (1 α t (3 4 α t (1 4 α t(1 t γ ε 1 α ( t 3(3 t 3(1 4 α t (5 4 α t(1 γ CS 1 t(1 4 αt (3 4 αt Smlarly, e can derve the socal elfare ( SW derved from roduct as: SW SW ( α y 1 1 1 y t dy y t ddy 0 ( (1 ( (1 (1 γ (1 y t α y 1 1 1 1 γ y t ddy y t dy y ε y ε y ε (1 γ (1 y t y γ ε (56 The total socal elfare SW SW SW. y substtutng the otmal retal rces from emma 1, e have. (1 α t (3 4 α t SW 3 t(4 t( γ ε 3(1 4 α t (1 γ 1 t(1 4 αt(3 4 αt When 0, CS f and only f CS αt t(9 4 αt t[3 8 αt(1 α t] [1 8 αt(1 αt] γ ε <0 3 (1 4 αt 8(1 4 αt 8(1 4 αt 1 t(1 4 αt hch leads to the condton n Inequalty (1. SW f and only f SW αt t[1 4αt 4 α t(1 α t] [1 8 α t(1 α t] γ ε (1 4 αt 4(1 4 αt 1 t(1 4 αt hch leads to the condton n Inequalty (. Proof of emma Proof. We denote a 1 (1 γ ( τ, a 1 (1 γ ( τ, b 1( τ α, and c 1( τ. The demand functons n Equaton (8 then can be rertten as MIS Quarterly Vol. 41 No. 3 endsetember 017 5

Kark et al. Strategc Tool for Onlne etalers a b c a b c (57 The retaler s otmzaton roblem n stage s characterzed by the frst-order condtons of Equaton (3: a b c c( b( 0 a b c c( b( 0 from hch e can derve the retaler s otmal retal rces as functons of the holesale rces: a b a c ( b c a b a c ( b c The manufacturers otmzaton roblems n stage 1 are characterzed by the frst-order condtons of Equaton (4: (58 1 ( a b c 0 1 ( a b c 0 from hch e can derve the otmal holesale rces: ab ac 4b ab ac 4b c c (59 Substtutng the above otmal holesale rces nto Equaton (58, e derve the otmal retal rces: ab ac ab ac (4 b c ( b c ab ac ab ac (4 b c ( b c (60 Wth the above equlbrum demands, the otmal holesale rces n Equaton (59, and the otmal retal rces n Equaton (60, e have the retaler s equlbrum roft: π ( ( 3 ( a a b ( a b a c( a b a c b 4( b c ( b c ( b c(4 b c (61 emma follos by substtutng a, a, 6 MIS Quarterly Vol. 41 No. 3 endsetember 017 a, b, and c nto the above otmal holesale rces and retal rces. Smlarly, by substtutng a, b, and c nto Equaton (61, the retaler s roft can be derved as

Kark et al. Strategc Tool for Onlne etalers π (1 ατ (1 ατ (1 γ 8 α(1 4 ατ 8 τ(1 ατ(3 4 ατ (6 Proof of Prooston 3 Proof. (a We notce ε (3 4 αε (1 γ (1 4 αγε (3 4 αγε (1 γ f and only f ε (3 4 αε (1 γ (1 4 αγε (3 4 αγε hch leads to the condton n Inequalty (9. (b Substtutng τ γε nto Equaton (6, e have the retaler s roft. (1 γ because We notce (1 αγε 4ε (1 γ 3 γ(3 αε(6 γ(7 αε(6 γ(3 4 αε >0 3 3 (1 γ 8 ε (1 4 αγε γ (1 αγε (3 4 αγε ε [15 αε(17 γ(18 αε(0 γ(11 1 αε] (1 γ (1 4 αγε 4(1 αγε (3 4 αγε (1 γ f and only f ε [15 αε(17 γ(18 αε(0 γ(11 1 αε] (1 γ (1 4 αγε 4(1 αγε (3 4 αγε hch leads to the condton n Inequalty (30. Proof of Corollary 6 Proof. s under the latform scheme, e can smlarly derve the consumer surlus ( CS and socal elfare ( SW by substtutng the otmal retal rces n emma nto Equatons (53 and (54, resectvely: (1 αγε t (1 αγε (1 6 αγε tα (1 6 αγε (1 γ (1 αγε(5 6 αγε CS (1 4 αγε 8 α (1 4 αγε 4α ( 1 4αγε 8 γε (1 αγε (3 4 αγε t t γε (1 αγε (3 4 αγε (1 6 αγε α (1 γ (1 4 αγε (5 6 αγε (1 8 αγε (1 αγε 6γε 6(1 4 αγε 4 γ ε (1 αγε (3 4 αγε (1 γ (1 8 αγε (1 αγε MIS Quarterly Vol. 41 No. 3 endsetember 017 7

Kark et al. Strategc Tool for Onlne etalers ( ( (1 αγε 6γε 3γε t t (1 αγε γ ε (1 αγε (3 4 αγε (1 γ (1 4 αγε (1 8 αγε (1 αγε SW 1γε 1 4αγε 1 4 αγε (1 4 αγε 4 γ ε (1 αγε (3 4 αγε (1 γ (1 8 αγε (1 αγε When 0, CS (1 γ because 3 3 CS αε t 1 8 αγε(1 αγε 1 αγ ε t(1 4 αγε(6 αγ ε 3 (1 γ (1 4 αγε 1 γ ε (1 4 αγε 1 γ ε (1 4 αγε and e can verfy that the above s ostve usng a condton that even the consumer th a sgnal ndcatng the largest degree of msft has ncentve to urchase. SW (1 γ because SW ( t αε t 1 8 αγε (1 αγε (1 γ (1 4 αγε 1 γ ε(1 4 αγε Proof of Prooston 4 Proof. (a We notce t 4 αt(1 γ (1 4 tα (3 4 tα f and only f t 4 αt(1 γ (1 4 tα (3 4 tα hch leads to the condton n Inequalty (31. (b Substtutng τ t nto Equaton (6, e have the retaler s roft. because (1 αt (1 γ 3 4 αt(3 αt(3 αt 4t 3 3 8 t(1 αt (3 4 αt (1 4 αt We notce t αt[17 8 αt(5 3 αt](1 γ (1 4 αt 4(1 αt (3 4 αt f and only f t αt[17 8 αt(5 3 αt](1 γ (1 4 αt 4(1 αt (3 4 αt hch leads to the condton n Inequalty (3. 8 MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers Proof of Corollary 8 Proof. s under the latform scheme, e can smlarly derve the consumer surlus ( CS and socal elfare ( SW by substtutng the otmal retal rces n emma nto Equatons (55 and (56, resectvely: (1 α CS (1 α (1 6 α ( (1 6 α (1 α [11 4 α (5 α ](1 γ (1 4 αt 4 8 α (1 4 αt 8(1 4 αt 16 t(1 αt(3 4 αt γε γε[ t(1 αt (3 4 αt (1 6 αt α(1 4 αt(5 6 αt (1 8 αt(1 αt(1 γ ] 1t 1(1 4 α t 4 t (1 αt (3 4 αt (1 8 αt(1 αt (1 γ t t t t t t t t t t (1 α t (1 α t 3( t γ ε t (1 α t(3 4 αt (1 4 α t(1 8 α t(1 α t(1 γ SW [ (1 4 α t 6 t 4 t (1 α t (3 4 α t (1 8 α t(1 α t (1 γ 16 t(1 α t(3 4 α t ( t(1 α t(3 4 α t (1 8 α t(1 α t(1 γ (1 8 α t(1 α t t(3 4 α t (1 4 α t(1 γ 4 t( 1 α t(3 4 α t (1 8 α t(1 α t(1 γ (1 γ 16 (1 α (3 4 α ( (1 α (3 4 α (1 8 α (1 α (1 γ (1 8 α t(1 α t t(3 4 α t (1 4 αt(1 γ 4 t(1 α t(3 4 α t (1 8 α t(1 α t(1 γ (1 γ t t t t t t t t ] When 0, CS f and only f CS αt [1 8 αt(1 αt] γ ε t[1 4 αt(1 ( αt( (3 4 αt] <0 3 (1 4 α t 4 t(1 4 α t 8(1 4 α t hch leads to the condton n Inequalty (33. SW f and only f SW αt 3 t 1 4 αt(1 α t 1 8 α t(1 α t γ ε <0 (1 4 αt 4 t(1 4 αt hch leads to the condton n Inequalty (34. Proof of Prooston 5 Proof. When 0, the latform scheme generates more roft for the retaler than holesale scheme f and only f (1 ατ (1 6 ατ 8 α (1 4 ατ ( μ μ π π 8 α(1 4 ατ (63 hch leads to the condton n Inequalty (35. When >0, e can rerte Inequalty (63 as (1 6 ατ (1 ατ (1 γ (7 6 ατ(1 ατ π π ( μ μ 8 α (1 4 ατ 8 τ (1 ατ (3 4 ατ Therefore, π < π f and only f MIS Quarterly Vol. 41 No. 3 endsetember 017 9

Kark et al. Strategc Tool for Onlne etalers τ > ατ ατ ατ ατ α ατ μ μ α (1 4 ατ (1 γ (1 ατ (7 6 ατ (1 (3 4 (1 (1 6 8 (1 4 ( Proof of Prooston 6 Proof. (a Under latform scheme, based on Equaton (5, e have (1 γ (1 ατ τ(3 4 ατ Under holesale scheme, based on Equaton (6, e have (1 γ (1 ατ 4 τ(1 ατ(3 4 ατ (b From the above dervatves, e have ( π π (1 γ (1 ατ (1 ατ τ(3 4 ατ 4(1 ατ Proof of Prooston 7 Proof. In the qualty-domnates-ft case th 0, CS < CS because (1 αγε α(1 4 αγε (6 γε 3γε 6αγ ε 6 αγε (1 4 αγε t t CS CS 4 αγε (1 4 αγε and e can verfy that the above s negatve usng a condton that even the consumer th a sgnal ndcatng the largest degree of msft has ncentve to urchase. SW < SW because t t SW SW 1 γε (1 4 αγε 3 γε (1 αγε <0 In the ft-domnates-qualty case th 0, CS < CS because (1 α t 1 α t(1 4 αt 3t 3 t( αt( (1 4 αt( α(1 4 αt γ ε CS CS 4 αt(1 4 α t and e can verfy that the above s negatve usng a condton that even the consumer th a sgnal ndcatng the largest degree of msft has ncentve to urchase. SW < SW because (1 αt 1 t 3 t ( γ ε (1 α t 3 t 9 α(3 4 αt t α(1 4 α t γ ε SW SW <0 4 t(1 4 αt 4 αt(1 4 αt here the second nequalty s by alyng a condton that even the consumer th a sgnal ndcatng the largest degree of msft has ncentve to urchase. 10 MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers nalyss of Model Etensons Proof of emma 3 and esults on the Effects of Precson Imrovement under Non-Zero Qualty fference Proof. The roof s the same as that of emma 1, ecet that e no have denote a 1 [ γδ (1 γ ]( τ and a 1 [ γδ (1 γ ]( τ. y substtutng a, a, b, and c nto the otmal retal rces, commsson rate, and fed fee derved n the roof of emma 1, e obtan the results n emma 3. Smlarly, e can derve the retaler s roft as (1 ατ τ γ δ (1 γ γδ (1 γ π μ μ τ (1 4 ατ (3 4 ατ (3 4 ατ (a In qualty-domnates-ft case th δ : (1 γ because (1 γ f and only f ε 4αεδ (1 γ (1 4 αγε (3 4 αγε ε 4αεδ (1 γ (1 4 αγε (3 4 αγε That s, (1 γ f and only f δ <(3 4 αγε [4 α(1 4 αγε ]. (1 γ f and only f π ε δ 3 4 αγε(3 4 αγε 3 3 (1 γ (1 4 αγε γ ε(3 4 αγε That s, (1 γ f and only f 3 3 δ < γ ε (3 4 αγε [(1 4 αγε (3 1αγε 16 α γ ε ]. ll together, e can conclude that the results on the effects of recson mrovement reman the same as n Prooston 1 hen δ s small. (b In ft-domnates-qualty case th δ : because t 4αδ t (1 4 αt (3 4 αt f and only f t 4αδ t (1 4 αt (3 4 αt MIS Quarterly Vol. 41 No. 3 endsetember 017 11

Kark et al. Strategc Tool for Onlne etalers That s, f and only f δ <(3 4 αt [4 α(1 4 αt ]. f and only f π t δ 3 4 α t(3 4 α t. 3 3 (1 4 αt t(3 4 αt That s, f and only f 3 3 δ < t (3 4 αt [(1 4 αt (3 1αt 16 α t ]. ll together, e can conclude that the results on the effects of recson mrovement reman the same as n Prooston hen δ s small. Proof of emma 4 and esults on the Effects of Precson Imrovement under Non-Zero Qualty fference Proof. The roof s the same as that of emma, ecet that e no have a 1 [ γδ (1 γ ]( τ and a 1 [ γδ (1 γ ]( τ. y substtutng a, a, b, and c nto the otmal holesale rces, retal rces, and retaler roft derved n the roof of emma, e obtan the results as n emma 4. Smlarly, e can derve the retaler s roft as π (1 ατ (1 ατ γδ (1 γ 8 α(1 4 ατ 8 τ(1 ατ(3 4 ατ (a In qualty-domnates-ft case th δ : (1 γ because ε 4αεδ (1 γ (1 4 αγε (3 4 αγε (1 γ f and only f ε 4αεδ (1 γ (1 4 αγε (3 4 αγε That s, (1 γ f and only f δ <(3 4 αγε [4 α(1 4 αγε ]. (1 γ because ε αεδ[17 8 αγε(5 3 αγε] (1 γ (1 4 αγε 4(1 αγε (3 4 αγε (1 γ f and only f 1 MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers ε αεδ[17 8 αγε(5 3 αγε]. (1 γ (1 4 αγε 4(1 αγε (3 4 αγε That s, (1 γ f and only f δ <(1 αγε(3 4 αγε [ α(1 4 αγε(17 40αγε 4 α γ ε ]. (1 γ because π ε (1 αγε (1 αγε [3 4 αγε (3 αγε (3 αγε ] δ 3 3 (1 γ (1 4 αγε 8 γ ε (1 αγε (3 4 αγε ll together, e can conclude that the results on the effects of recson mrovement reman the same as n Prooston 3 hen δ s small. (b In ft-domnates-qualty case th δ : because t 4αδ t (1 4 αt (3 4 αt f and only f t 4αδ t (1 4 αt (3 4 αt That s, f and only f δ α α α <(3 4 t [4 (1 4 t ]. because t αtδ [17 8 αt(5 3 αt] (1 4 αt 4(1 αt (3 4 αt f and only f t αδ t [17 8 αt(5 3 αt]. (1 4 αt 4(1 αt (3 4 αt That s, f and only f δ α α α α α α < (1 t (3 4 t [ (1 4 t (17 40 t 4 t ]. because π t(1 αt (1 αt[3 4 αt(3 αt(3 αt] δ 3 3 (1 4 αt 8 t(1 αt (3 4 αt ll together, e can conclude that the results on the effects of recson mrovement reman the same as n Prooston 4 hen δ s small. MIS Quarterly Vol. 41 No. 3 endsetember 017 13

Kark et al. Strategc Tool for Onlne etalers Proof and esults on the Effects of Precson Imrovement under fferent Precsons mong Consumers Proof. (a Effect of Thrd-Party Informaton under Platform Scheme enotng the notatons as a a ( a a, b ( a a ( τ ( a a α, and c ( a a ( τ hen 0, e can relcate the same rocess as n the roof of emma 1. ecause a a 1, t s easy to see that all terms are reduced to those n our baselne model by relacng τ th a ne term τ, τ ( a a τ τ [ aτ a τ ], here τ { γ ε, } and τ { γ ε, } t t th τ γ ε for the qualty-domnates-ft case and τ t for the ft-domnates-qualty case. Therefore, e can obtan the otmal retal rces and the retaler s roft: τ 1 4ατ (1 ατ τ π μ μ (1 4 ατ Notce that n emma 1 n our base lne model, τ γε n the qualty-domnates-ft case and τ t n the ft-domnates-qualty case, here τ γ ε n the qualty-domnates-ft case and τ t n the ft-domnates-qualty case. In the case th dfferent recsons across consumers, t s also found that τ γ a ( a a γ ε ( a γ a γ and τ γ γ ε γ γ > n the qualty-domnates-ft case and a ( a a ( a a 0 τ a ( a a t ( a a and τ a ( a a t ( a a n the ft-domnates-qualty case. ecause the sgns of the mact of recson arameters on τ n the baselne model and τ n the the model th heterogeneous recsons are the same, and the equlbrum quanttes n the to models dffer only on ths varable, t s easy to see the effect of the mroved recson from the thrd-arty nformaton s qualtatvely same n both these models. We net sho the detaled analyss under the latform scheme. (a.1 In the qualty-domnates-ft case: (1 γ because a εγ (1 γ a γ a γ 4αεγ γ (1 γ because a εγ (1 γ a γ a γ 4αεγ γ (1 γ because (1 γ because 14 MIS Quarterly Vol. 41 No. 3 endsetember 017 a ( a a ( a a π εγ γ γ 3 (1 γ γ γ 4αεγ γ

Kark et al. Strategc Tool for Onlne etalers π a εγ a γ a γ 3 (1 γ a γ a γ 4αεγ γ (a. In the ft-domnates-qualty case: >0 because a t a a 4α t >0 because a t a a 4α t >0 because a t( a a ( a a 4 t π 3 α >0 because (b Effect of Thrd-Party Informaton under Wholesale Scheme a t( a a ( a a 4 t π 3 α Smlarly, usng the notatons defned a a ( a a, b ( a a ( τ ( a a α, and c ( a a ( τ hen 0, e can relcate the same rocess as n the roof of emma. elacng τ th τ ( a a τ τ [ aτ a τ ], here τ { γ ε, } and τ { γ ε, } th τ γ ε for the qualty-domnates-ft case and τ for the ft-domnates-qualty case, t t e can smlarly derve the equlbrum outcomes. The otmal holesale rces, retal rces, and the retaler s roft are obtaned: τ 1 4ατ 1 6ατ 4 α(1 4 ατ t π (1 ατ 8 α(1 4 ατ s shon under the latform scheme, e sho the analyss under the holesale scheme. (b.1 In the qualty-domnates-ft case: (1 γ because MIS Quarterly Vol. 41 No. 3 endsetember 017 15

Kark et al. Strategc Tool for Onlne etalers a εγ (1 γ a γ a γ 4αεγ γ (1 γ because a εγ (1 γ a γ a γ 4αεγ γ (1 γ because a εγ (1 γ a γ a γ 4αεγ γ (1 γ because a εγ (1 γ a γ a γ 4αεγ γ (1 γ because π a εγ a γ a γ αεγ γ 3 (1 γ a γ a γ 4αεγ γ (1 γ because π a εγ a γ a γ αεγ γ 3 (1 γ a γ a γ 4αεγ γ (b. In the ft-domnates-qualty case: >0 because >0 because >0 because a t a a 4α t a t a a 4α t a t a a 4α t 16 MIS Quarterly Vol. 41 No. 3 endsetember 017

Kark et al. Strategc Tool for Onlne etalers >0 because a t a a 4α t <0 because π a t a a α t 3 a a 4α t <0 because π a t a a α t 3 a a 4α t ll together, e can conclude that the man results from the baselne model stay the same quanttatvely and the nsghts carry over to the case th dfferent consumer recsons. MIS Quarterly Vol. 41 No. 3 endsetember 017 17