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

8 U i,0,d,t = ε i,0,d,t μ i,j,d 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 z j = v i v i = 1 z j = 1 z j = 1 j z j ν j,d j ν j,d j d ε i,j,d,t ν j,d N (0, τ 1 ν ) τ 1 ν l d ν j,d j l j j s j,l,d s j,l,d ν j,d N (z j + ν j,d, τ 1 s )

9 s j,l,d j l d z j + ν j,d j l j j τs 1 ν j,d t d z j ν j,d 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 + ( τ s n i,j,d,t + τ ν ) ( s i,j,d,t z j) v i t d I i,d,t {n i,d,t, s i,d,t, h i,d,t} n i,j,d,t j t s i,j,d,t

10 j h i,j,d,t j I i,d,t = {n i,d,t, s i,d,t, h i,d,t} t z j v i t s i,j,d,t v i τ s τ 1 ν n i,j,d,t n i,j,d,t = 0 j z j v i i d V (I t, ε t) = ( ε 0,t, j J t 0 {E (μ j I t) γ + ε j,t + δ V (I, ε ) f (I I t, j) g (ε ) di dε }) t δ f (I I t, j) I t j g (ε) ε f (I I t, j) I t {n t, s t, h t} t h t t = 1 ε i,j,d,1

11 j h h t j n t s t j l j l l j ω l,j j n t s t f (I I t, j) j j δ z j

12 R δ = 0 L

14 Table 1: t 60% 35% 5% 2.7 {.5,.5} D i i t = 1,, T d a i,d,t

15 Table 2: i d

16 Table 3: 0 1,140 1,923 1,912 2,873 4,076 1,746 6,627 11,013 11,072 14,137 33, , ,113 4,906 4,482 6,336 9, ,068 1,769 n i,j,d,t ω

17 i j i j j 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 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 i (a > 0 n a > 0) i (a > 0 n a = 0) i a n a > 0 Δ i = i (a > 0 n a > 0) i (a > 0 n a = 0) i Δ i > 0 Δ i < 0 Δ i 0 t = 2 t = 1 t = 2 Δ i Δ i < 0 Δ i > 0 (a = j n j > 0) (a = j n j = 0) l l = 1,, 50 Δ i < 0 Δ i > 0

18 Figure 1: Share of consumers Sample Step 2 5 choices Step 2 choices only -25% 0% 25% 50% Difference in average visit probability when links are observed (Δ i ) x Δ i t > 1.3% 3.6% 3.7% μ i,j,d γ i ε i,j,d,t j) d t

19 t β i,j,d,t U i,j,d,t = μ i,j,d + β i,j,d,t γ i + ε i,j,d,t β i,j,d,t 0 β i,j,d,t 0 β i,j,d,t μ i,j,d d N

20 λ i > 0 K i,d,t j K +j i,d,t j K +j i,d,t K i,d,t i j t i j t d β i,j,d,t = λ i ( K+j i,d,t K i,d,t). K i,d,t j K +j i,d,t j b j 1 (1 π b) α j π b U (0, 1) b α j (0, 1) j α j j t d K +j i,d,t K i,d,t K +j i,d,t K i,d,t K i,d,t, h i,d,t Binom { N K i,d,t, J A (h) = h k α k k=1 α j 1 + A (h i,d,t) + α j } h i,d,t {0, 1} J A (h) α j

21 N K i,d,t α j/ (1 + A (h i,d,t) + α j) j j t d E (β i,j,d,t I i,d,t) = λ i [( 1 + A (h i,d,t) + α j ) ( N K i,d,t) ] I i,d,t K i,d,t α j I i,d,t {n i,d,t, s i,d,t, h i,d,t, K i,d,t} j λ i α j λ i K i,d,t A (h) α j α j α j K words j,d w j,d (1 + words j,d) w j,d K i,d,1 d j K i,d,1 i j d w j,d K i,d,1 i K i,d,1 d

22 v i λ i γ i D i v i N (η v + D i φ v, ζv 2 ), λ i N (η λ + D i φ λ, ζλ) 2, γ i N (η γ + D i φ γ, ζγ 2 ) γ i γ i,d = γ i (γ w) γ i d γ w > 0 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 (μ i,d,j I i,d,t) + E (β i,d,j,t I i,d,t) γ i,d + δ k J i,d,t j [V k (I )] f (I I i,d,t, k) di j t j ε i,d,j,t θ a = {a i,d,t} I = {I i,d,t} L (θ a, I, ω, w) i d T i,d t j Ji,d,t { [V j (I i,d,t θ)] 1 + ȷ J i,d,t [V ȷ (I i,d,t θ)] } 1(a i,d,t =j) I K s

23 Table 4: (z j, α j) 5 2 (φ v, φ λ, φ γ) 7 3 v i λ i γ i (η λ, η γ) 1 2 (ζ λ, ζ γ) 1 2 γ w 1 1 τ s 1 1 δ 1 1 L (θ a, ω, n, w, h) n ω w h K s γ i z j

24 v i τ s 0, 1, α j λ i δ L R L L L R L R R L R L R

25 N K i,d,t λ i N N = 30 τ ν = 1 τ s /τ ν j z j = 0 η v = 0 ζ v = 1 δ τ s

26 Table 5: , , , δ = , , , δ = 0 τ s = , , , Table 6: δ = δ = 0 τ s = k (n)k k n Table 7: z α z j α j (0.003) (0.007) (0.002) (0.003) (0.002)

27 Figure 2: α j z j Average vertical quality (α j ) egotastic dlisted celebuzz thesuperficial Average horizontal match location (z j ) perezhilton Posterior density: Figure 3: Average remaining match uncertainty 100% 95% 90% 85% 80% Number of links observed y n = 0,, 4 x (μ j,d n j,d = 0,, 4) / (μ j,d n j,d = 0) (τ s n + 1) 1

28 Table 8: v λ γ (0.18) (0.26) (0.10) (0.19) (0.25) (0.10) (0.32) (0.50) (0.17) (0.24) (0.37) (0.14) (0.24) (0.34) (0.12) (0.24) (0.33) (0.12) (0.36) (0.52) (0.20) η (0.36) (0.14) ζ (0.10) (0.04) % 16.0% 6.0%

29 i j z j v i τ s z j x v i z j < 0 z j > 0 τ s τ s (0.01, 0.22) 0.06 τs 1/2

30 5.2 (2.1, 10.3) α j y λ i γ i γ i γ w δ )

31 0.001, 0.645) z j α j ω j x y z j x z j α j

32 Figure 4: Average vertical quantity ( α ) E D C S Average horizontal match location ( z ) P Link frequency: 20% 40% 60% ω z α S S S ω n ω S S = 500

33 Table 9: 0.59% 0.11% 0.14% 0.05% 0.54% 0.06% 0.10% 0.18% 0.14% 0.09% 0.01% 95% 0 y E θ [(y baseline y counter ) /y counter ].59%.14%.54%

34 Table 10: t > 1 t = 1 t > % 0.45% 0.04% 0.01% 0.21% 0.42% 0.26% 0.02% 0.03% 1.32% 0.08% 0.00% 0.21% 0.55% 0.47% 0.14% 0.76% 0.14% 0.27% 0.03% 0.11% 0.07% 0.14% 0.02% 95% 0.18%.14% ω n t = 1 t = 1 t = 1

35 t = 1.03% 1.32%.26% 3.8%.14% 2.3%.05% L R d L d R

36 .14% 2.3%

37 .05%

38 archive.org/web/ / https: //web.archive.org/web/ / / actividades / informe - economico - del - impacto - del - nuevo - articulo de-la-lpi-nera-para-la-aeepp.html

39 org/files/2016/07/pj_ _modern-news-consumer_final.pdf N i d i d b j j

40 π b (0, 1) b α j (0, 1) j b j 1 (1 π b) α j j α j 1 b j π b j α j 0 b j α j j π b π b U (0, 1) α t α j t b t 1 (1 π b) α 1 (1 π b) α t 1 = (1 π b) A t A t A (h t) α j π b π b (1 π A t b) p (π b A t) = 1 0 (1 π A = t (1 π b) At (1 + A t) = Beta (π b 1, 1 + A t) b) dπ b b j π b b j [b j b ] = 1 α (1 (1 π b) αj ) (1 π b) At j (1 + A t) dπ b = α j + A t j N K t α j/ (1 + α j + A t) I t {n t, s t, K t, h t} A t j h t,j α j

41 I I t j f (I I t, j) = f (n, s, K, h n t, s t, K t, h t, j) f (I I t, j) = p (s n, n t, s t) p (n n t, j) p (K K t, h t, j) p (h h t, j) p (K K t, h t, j) h j δ x x p (h h t, j) = δ 1 (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 +1 ( n ȷ ) + (1 ω j,ȷ ) δ nt,ȷ ( n ȷ ) ȷ s ȷ s ȷ = s t,ȷ p ( s j n j, n t,j, s t,j) = N z ( j + τsn t,j[s t,j z j], τ τ s n t,j +τ s 1 + ν [n t,j τ s + τ 1 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,1 E [K i,d,1] = Nα j /(1 + α j ) w j,d K i,d,1 K i,d,1 E [K i,d,1 w j,d] = N q (w j,d) q (w j,d) j d K i,d,1 K i,d,t t > 1 q (w j,d) q (w j,d)

42 w j,d ( 0, 1 2) α j (0, 1) α j/ (1 + α j) ( 0, 1 2) 2 q (w j,d) = 1+( w j,d c) 1 c 3 {w j,d} d i K i,d,1 = 0 {w j,d} i K i,d,1 = N/2 E (μ i,1) γ i a i,1 ω 1 E (μ i,1) γ i E (μ i,1) ε i,j,d,1 z j v i δ ω ω δ = 0 t = 2 ω 2 w i,1 t > 2

43 a i,2 n i,1 τ s /τ ν ν j,d s j,l,d ν j,d s j,l,d ε i,j,d,t α j λ i v i λ i γ i D i γ w j t n i,j,t j ε i,j,d,t j s ν j,d ε i,j,d,t ν j,d n i,j,t n i,j,t ε i,j,d,t j k s k,j,d ε i,j,d,t s k,j,d n i,j,t ε i,j,d,t ν j,d n i,j,t ν j,d j j j

44 Table 11: E (μ i,1) γ i a i,1 ω 1 z j v i E (μ i,1) δ (a i,1, a i,2,, ω 1, ω 2, ) ω τ s/τ ν (a i,2, n i,1) ω 2, w i,1 ν s E (β i,2) (a i,2, w i,1) ω 2, n i,1 K α j λ i E (β i,2) φ v v i D i v i φ λ η λ ζ 2 λ λ i D i λ i φ γ η γ ζγ 2 γ i D i γ i γ w (a i,1, weekend) a i,1 a i,2 ω 1 ω 2 w i,1 n i,1 E (μ i,1) E (β i,2) t = 2 ε i,j,d,t s k,j,d n i,j,t j k j j j k k N λ i N λ i N = 30 ν j,d s j,k,d τ ν = 1 τ s z j v i z j v i

45 v i η v = 0 ζ v = 1 K s s s j,l,d (s j,l,d z j ν j,d) τs 1/2 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 α j N (0, 1), z j N (0, 1), τ 1/2 s Ga (.4, 5) E (τ 1/2 s ) = 2, η λ N (1,.5), η γ N ( 1,.5) φ ζ N (0, ζ 2 ), φ v N (0, 1), ζ 2 χ 2 (10,.4), γ w N (0, 1) δ U (0, 1)

46 f (x) f (x) f (x) z j α j

47 Table 12: z j α j z j α j z j α j z j α j z j α j α j z j

48 δ = 1 τ s =.2 τ s = 2 γ = 2 v = 2 z = 0 ω L,R = 1 ω R,L = 0 Figure 5: Probability of initiating a session (No links) Noisy Informative Links Behavior Myopic Forward looking

49 Figure 6: Share of sessions starting at linking site (No links) Noisy Informative Links Behavior Myopic Forward looking Figure 7: Number of sites visited during session (No links) Noisy Informative Links Behavior Myopic Forward looking

50 Figure 8: 0.62 Share of sessions visiting linked site (No links) Noisy Informative Links Behavior Myopic Forward looking Figure 9: Conditional probability of visiting the linked site Myopic Forward looking (No links) Noisy Informative (No links) Noisy Informative Links Signal Lower than expected match (No links) Higher than expected match

51 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

52 Θ W t θ θ (t 1) b θ p(θ W ) D θ // [1] (m, S) f(θ, D θ ) // [2] θ c N(m, S) p(θ c W ) D θ c // [1] (m, S ) f(θ c, D θ c) // [3] α p(θc )N(θ m,s ) p(θ)n(θ c m,s) 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) ) // [4] W { W, I, θ (t) } Θ θ (t)

Introduction Benchmark model Belief-based model Empirical analysis Summary. Riot Networks. Lachlan Deer Michael D. König Fernando Vega-Redondo

Introduction Benchmark model Belief-based model Empirical analysis Summary. Riot Networks. Lachlan Deer Michael D. König Fernando Vega-Redondo Riot Networks Lachlan Deer Michael D. König Fernando Vega-Redondo University of Zurich University of Zurich Bocconi University June 7, 2018 Deer & König &Vega-Redondo Riot Networks June 7, 2018 1 / 23