3% 5% 1% 2%

d t = 1,, T d i j J i,d,t J i,d,t+ = J i,d,t j j a i,d,t j i t d γ i > 0 i j t d U i,j,d,t = μ i,j,d + β i,j,d,t γ i + ε i,j,d,t ε i,j,d,t t ε i,,d,t μ β μ μ i,j,d d t d, t

j μ i,j,d i j d z j ν j,d v i μ i,j,d = z j + ν j,d v i sign z j = sign v i v i = 1 z j = 1 z j = 1 j z j ν j,d j d ν j,d N 0, τ ν τ ν l ν j,d l j j s j,l,d ν j,d N z j + ν j,d, τ s s j,l,d s j l d τ s ω l,j l j ω l,j ω j,l ω

τ s n i,j,d,t E μ i,j,d I i,d,t = z j v i + s τ s n i,j,d,t + τ i,j,d,t z j v i ν t d n i,j,d,t j t s i,j,d,t I i,d,t t n s I i,d,t z j v i t s i,j,d,t v i τ s τ ν n i,j,d,t n i,j,d,t = 0 j z j v i. β β β R + β i,j,d,t F d I i,d,t, λ i, α j

α j (0, 1) j α j λ i i F d I i,d,t t d j i j t d E β i,j,d,t I i,d,t = α j N K i,d,t 1 + A i,d,t + α j K i,d,t λ i + u κ + K i,d,t λ i i,d,t j t d A i,d,t α j K i,d,t u i,d,t N

κ j j α j /(1 + A i,d,t + α j ) j α j A i,d,t j α j N K i,d,t j λ i u i,d,t μ β i d μ β V(I t, ε t ) = max ε,t, j J t E β j,t I t + E μ j I t γ + ε j,t +V(I, ε ) f I I t, j g (ε ) di dε t I t n t, s t, K t, h t, u t

f I I t, j I t j h t A t j h j,t α j g (ε) ε n t s t K t h t u t h t+ h t j h j s t l ω l,j l l j n t,j = n t,j + 1 s t,j n t,j = n t,j s t,j = s t,j f j j j α j

ω j α j β = 0

60% 35% 5%

2.5 7.9 10.3 1.37 1.46 1.44 3.4 9.0 12.4 1.42 1.28 1.32 6.8 2.9 9.5 1.23 1.57 1.33 12.3 28.5 40.8 1.19 1.14 1.15 4.6 3.6 8.0 1.38 1.94 1.62 t Sites per session 3.0 2.5 2.0 1.5 1.0 2 sites 3 sites 4 5 sites 25 50 75 25 50 75 25 50 75 Sessions Male Female x y 2.7 {.5,.5} 0 1 2 2.89 D i i t = 1,, T d a i,d,t

......... x y

,,,,,,,,,,,,,,,,,,, i d n i,j,d,t ω w j,d log 1 + words j,d K i,d, w j,d i j

i j j Pr i a = j n i,j > 0 = d t 1 a i,d,t = j n i,j,d,t > 0 d t 1 n i,j,d,t > 0 i j Pr i a = j n i,j = 0 = d t 1 a i,d,t = j n i,j,d,t = 0 d t 1 n i,j,d,t = 0 i Pr i (a > 0 n a > 0) Pr i (a > 0 n a = 0) i a n a > 0 Δ i = Pr i (a > 0 n a > 0) Pr i (a > 0 n a = 0) i Δ i > 0 Δ i < 0 Δ i 0 Δ i 39% Δ i < 0 31% Δ i = 0 30% Δ i > 0 40% Pr a = j n j > 0 Pr a = j n j = 0 2.0% l l = 1,, 50 Δ i < 0 Δ i = 0 Δ i > 0

Cumulative share of consumers 100% 75% 50% 25% 0% 0.1 0.0 0.1 0.2 0.3 Difference in probability of visiting linked site after seeing one or more links ( i ) x i 5.6% v i λ i γ i D i v i N η v + D i φ v, ζ v, log λ i N η λ + D i φ λ, ζ λ, log γ i N η γ + D i φ γ, ζ γ γ i γ i exp γ w γ i,d = γ i d γ w > 0

α j w j,d i K i,d, d i K i,d, w j,d j K i,d,t α j K i,d,t K i,d, K i,d, t = 1 K i,d,t t > 1 α j α j ε i,d,j,t EV (0, 1) j I i,d,t V j I i,d,t + ε i,d,j,t V j I i,d,t V j I i,d,t = E β i,d,j,t I i,d,t + E μ i,d,j I i,d,t γ i,d + log exp V ȷ (I ) f I I i,d,t, ȷ di ȷ J i,d,t j j t j ε i,d,j,t θ

z j, α j φ v, φ λ, φ γ v i λ i γ i η λ, η γ ζ λ, ζ γ γ w τ s a = a i,d,t I = I i,d,t T i,d exp V j I i,d,t θ L (θ a, I) 1 + ȷ exp V J ȷ I i,d,t θ i,d,t i d t j J i,d,t 1a i,d,t =j I u K s L (θ a, n, w, h) n w h u K s u K s (θ, I) p (θ D) θ p (θ a, n, h, w, D) L (θ a, I) f (I n, h, w) p (θ D) ds du dk

z j φ v τ s α j α j α j η λ φ λ ζ λ α j α j α j η λ α j φ λ ζ λ η γ φ γ ζ γ γ w N = 30 κ = 4 τ ν = 1 j z j = 0 η v = 0

ζ v = 1 α j

f (x) f (x) f (x) i j z j v i τ s

α j z j Information quantity ( α ) 0.2 0.1 0.0 egotastic dlisted thesuperficial celebuzz perezhilton 2 1 0 1 2 Match location ( z ) Posterior density 0.1 0.2 0.3 v λ γ... (.) (.) (.)... (.) (.) (.)... (.) (.) (.)... (.) (.) (.)... (.) (.) (.)... (.) (.) (.)... (.) (.) (.) η... (.) (.) ζ... (.) (.).......%.%.%

Match uncertainty remaining 100% 90% 80% 70% 60% 0 1 2 3 4 Number of links observed y n =,, x μ j,d n j,d =,, μ j,d n j,d = (τ s n + ) z j x 1.85 0.58 0.18 0.43 1.82 z j z j < 0 z j > 0 v i v i z j < 0 z j > 0

τ s τ s 217 α j y λ i α j λ i α j λ i λ i α j λ i α j α j

γ i log γ i γ w z j α j ω j x y z j z j z j 0 z j x

Information quantity ( α ) 0.25 0.20 0.15 0.10 0.05 0.00 E D 2 1 0 1 2 Match location ( z ) Link frequency: 20% 40% 60% S C P

S 3 5 = 15 S S ω n ω S = 200

.......... a..............., a..............., a..... % a................ a., a, a. X Y Y X X X t = % a

0.25% 2% 2% 2% 2% 0.5% 0.35%

t t + 1 3.2% 5.5% 0.2% 0.3% 0.67% 2.5% 79% 71% 0.47% 0.07% 2.11% 0.34%

d N N t j k t {0, 1} N k b, = 0 b j ι j {0, 1} N u R N + d i j t N β j,t = u b ι j,b 1 k b,t b= u ι j β j,t = K u K t u t K t = N k b= b,t t u t = N u K t b= bk b,t K u j K t u t K u j K u

ι j u ι j j u b j j π b [0, 1] α j (0, 1) j b j Pr[ι j,b = 1 π b ] ρ j,b ρ j,b Pr ι j,b = 1 π b = 1 (1 π b ) α j j α j 1 ρ j,b π b j α j 0 π b > ρ j,b 0 α j j u b σ σ u b σ Expo σ d σ u b ι j u b σ π b ι j u b i.i.d. π b, Beta (α, 1), α > 0

k b,t = 0 π b,t k b,t = 0, h t Beta (α, 1 + A t ) h t t A t J j= h t,jα j α j j N K t EK K t I t, j = (N K t )1 Bα,+A t +α j B(α,+A t ) B (, ) I t t K t h t A t N K t j α α j α = 1 EK K t I t, j = (N K t ) α j +A t +α j i.i.d. σ InvGa (κ + 1, κ λ), κ > 0, λ > 0 λ i κ K t u t σ t I t InvGa (κ + K t + 1, κ λ + K t u t ) I t K t u t j

j α j E β j,t I t = +A t +α j (N K t ) λ + K t κ +K t (u t λ) K u I t u K, I t K I t u K, I t K K u K K t K t u t κ λ+k u κ λ+k t u κ+kt+ t κ λ+k u p u K, K, I t = > K K u t K t u t B(κ +K t +,K K t ) δ ut u K = K t K > K t u u = u t β j,t F β j,t I t, λ, α j = N Gaβ j,t K K t, λ + K t κ +K t (u t λ)binomk K t N K t, K =K t α j +A t +α j I t n t, s t, K t, u t, h t A t j h t,j α j I I t j f I I t, j = f n, s, K, u, h n t, s t, K t, u t, h t, j f I I t, j = p s n, n t, s t p n n t, j p u K, K t, u t p K K t, h t, j p h h t, j p u K, K t, u t p K K t, h t, j h j p h h t, j = δ h t,j, h h t h j 1 n s n ȷ j n ȷ n t,ȷ + 1 ω j,ȷ n t,ȷ 1 ω j,ȷ p n ȷ n t, j = ω j,ȷ δ nt,ȷ + n ȷ + 1 ω j,ȷ δ n t,ȷ n ȷ

ȷ s ȷ s ȷ = s t,ȷ N z p s j + τ sn t,j s t,j z j j n τ j, n t,j, s t,j = s n t,j +τ ν, τ s + n t,j τ s + τ ν, n j = n t,j + 1 δ st,j s j, n j = n t,j w j,d K i,d,t K i,d, E K i,d, = Nα j /(1 + α j ) i K i,d, K i,d, j d i K i,d, E K i,d, w j,d = N q w j,d q w j,d j d K i,d, K i,d,t t > 1 q w j,d α j (0, 1) q w j,d w j,d 0, qw j,d = 1 c w + w j,d c w w j,d d i K i,d, = 0 max w j,d i K i,d, = N/2 N κ λ i N κ λ i

κ N = 30 κ = 4 α j α α = 1 ν j,d s j,k,d τ ν = 1 τ s z j v i z j v i v i η v = 0 ζ v = 1 K u s u s σ σ σλ u u = uλ u λ s j,l,d s j,l,d z j ν j,d τ s s j,l,d z j ν j,d E s j,l,d = 0 V s j,l,d = 1 s ν j,d logit α j N (0, 1) z j N (0, 1) τ s Ga (.4, 5) E τ s = 2 η, φ ζ N 0, 10 ζ, ζ χ λ γ γ w N (0, 1) φ v N (0, 1)

................ z j α j 0.34 0.24 0.33 0.03

τ s =.2 τ s = 2 λ = 0 β = 0 γ = 2 v = 2 z = 0 ω L,R = 1 ω R,L = 0 Probability of initiating a session 0.300 0.275 0.250 0.225 (No links) Noisy Informative Links Behavior Myopic Forward looking

Share of sessions starting at linking site 0.56 0.54 0.52 0.50 (No links) Noisy Informative Links Behavior Myopic Forward looking Number of sites visited during session 1.175 1.150 1.125 (No links) Noisy Informative Links Behavior Myopic Forward looking

0.62 Share of sessions visiting linked site 0.60 0.58 0.56 0.54 (No links) Noisy Informative Links Behavior Myopic Forward looking Conditional probability of visiting the linked site 0.4 0.3 0.2 0.1 Myopic Forward looking (No links) Noisy Informative (No links) Noisy Informative Links Signal Lower than expected match (No links) Higher than expected match

p (θ W ) D θ D θ D θ D θ f (, ) θ θ D θ θ c θ c D θ c t θ c θ c θ θ π b,t k b,t = 0, h t Beta (α, 1 + A t ) h t t A t J j= h tα j α j α t α j t b t 1 (1 π b ) α (1 π b ) α t = (1 π b ) A t

Θ W t θ θ (t ) b θ p(θ W ) D θ μ, Σ f(θ, D θ ) θ c N(μ, Σ) p(θ c W ) D θ c μ, Σ f(θ c, D θ c) α p(θc )N(θ μ, ) p(θ)n(θ c μ,) u U(0, 1) u < α θ (t) b θ c θ (t) b θ I p(i θ (t) ) W f(i, θ (t) ) W { W, I, θ (t) } Θ θ (t)

π b b (1 π b ) A t π α b (1 π b ) [B (α, 1)] = (1 π b) (A t+) (1 π b) A t π α b (1 π b ) [B (α, 1)] dπ B (α, A t + 1) b Beta (α, A t + 1) π α b N K t j E K K t I t, j = (N K t ) 1 B α, 1 + A t + α j B (α, 1 + A t ) B (, ) I t t K t h t A t b j t ρ j,b,t π b,t = 1 1 π b,t α j π b,t E ρ j,b,t I t = 1 1 π b,t α j Beta π b,t α, 1 + A t dπ b,t = 1 B α, 1 + α j + A t B (α, 1 + A t ) N K t K t u t I t K t u t σ t I t InvGa (κ + K t + 1, κ λ + K t u t ) u b σ t K t K t u t σ t Ga (K t, σ t ) σ σ κ + K t + 1 κ λ + K t u t u b σ u u b u b

j j α j E β j,t I t = (N K t ) λ + (u 1 + A t + α j κ + K t λ) t K t E β j,t I t = E K u K t u t I t, j = E K E u K, I t I t, j K t u t E u K, I t = 1 K E [ σ t I t ] (K K t ) + u t K t = κ λ + K t u t 1 K t κ + K t K K t + u t K E β j,t I t = E K κ λ + K t u t κ + K t 1 K t K + u t K t K I t, j K t u t = E K K t I t, j κ λ + K t u t κ + K t E K K t I t, j u K, I t K K u K K t K t u t κ λ+k u κ λ+k t u κ+kt+ t κ λ+k u p u K, K, I t = > K K u t K t u t B(κ +K t +,K K t ) δ ut u K = K t β j,t K, σ t, I t Ga (K K t, σ t ) σ t I t InvGa (κ + K t + 1, κ λ + K t u t ) p β j,t, σ t K, I t σ t p β j,t K, I t = K K t κ +K t + β j,t κ β j,t +κ λ+k t u λ+k t u t t β t,j +κ λ+k t u t β t,j B (κ + K t + 1, K K t ) β j,t = u K u t K t u K K > K t

z 1 z 2 z 3 z 4 z 5 15 10 density 5 0 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 value α 1 α 2 α 3 α 4 α 5 400 300 density 200 100 0 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 value ζ λ 2 ζ γ 2 τ s 15 6 density 10 density 4 5 2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 value 0 1 2 3 4 5 value η λ η γ γ w 2 30 density 1 density 20 10 0 0 10 5 0 5 10 10 5 0 5 10 value 0.50 0.25 0.00 0.25 0.50 value

5 φ γ 1 φ γ 2 φ γ 3 φ γ 4 φ γ 5 φ γ 6 φ γ 7 4 density 3 2 1 0 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 value φ λ 1 φ λ 2 φ λ 3 φ λ 4 φ λ 5 φ λ 6 φ λ 7 1.5 density 1.0 0.5 0.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 value φ v 1 φ v 2 φ v 3 φ v 4 φ v 5 φ v 6 φ v 7 2.0 1.5 density 1.0 0.5 0.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 5.0 2.5 0.0 2.5 5.0 value