Switching Costs in Two-sided Markets - Ecares

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B Proof of Lemma 1∂p i 0,1∂s i= 8 3 δ is i + δ i − 2 3 δ F ,∂ 2 p i 0,1∂s 2 i= 8 3 δ i > 0,C Proof of Lemma 2∂p i 0,1∂s i| si =0 < 0 if δ i < 2 3 δ F .∂p i 0,1= δ i − 4δ is i (3 − ∆)− 2δ j(e j + 2e i )s j∂s i ∆∆Given that e A = e B = e, δ A = δ B = δ, µ i = 0,∂p i [0,1= δ 1 − 4s i(3 − ∆)∂s i ∆∂ 2 p i 0,1∂s 2 i− δ F ζ.− 6es ]j− 2 ∆ 3 δ F ,= − 4δ {i(3 − ∆) > 0 if e is small,∆ < 0 if e is large,[1 − 6es ]j< 2 ∆ 3 δ F .∂p i 0,1∂s i| si =0 < 0 if δD Proof of Proposition 6Differentiating Equation (3) with respect to α i , α j and δ F , we obtain the following:since∂p i 0,1{ ≤ 0, if µi → 1 or e i , e j small,∂α i > 0, if µ i → 0 and e i , e j large,∂p i 0,1∂α i> 0 ifµ i + 2(1 − µ i )s i1 + 2(1 − µ i )s i> ∆ 3 .∂p i 0,1∂α j≥ 0.∂p i 0,1∂δ F= −ξ i ≤ 0.22
E Proof of Proposition 7For part (i),∂p A 0,1= δ ∂s A 3 − 4δs A(3e 2 − 2)3(1 − e 2 ,)∂ 2 p A 0,1∂s 2 A= − 4δ(3e2 − 2)3(1 − e 2 )∂p A 0,1∂s A| sA =0 = δ 3 > 0.{ > 0 if e is small,< 0 if e is large,For part (ii), we compare the multi-homing model with the single-homing model withasymmetric switching costs. On the side with switching costs,p A mh < pA sh if e + v B2> 1,where mh denotes the multi-homing framework, and sh denotes the single-homing framework.On the side without switching costs,Referencesp B mh > pB sh if e + v B2> 1.[1] Simon Anderson, Øystein Foros, and Hans Jarle Kind. Competition for Advertisersin Media Markets. In Fourteenth CEPR/JIE Conference on Applied IndustrialOrganization, 2013.[2] Mark Armstrong. Competition in two-sided markets. RAND Journal of Economics,37(3):668–691, 2006.[3] Gary Biglaiser, Jacques Crémer, and Gergely Dobos. The value of switching costs.Journal of Economic Theory, 2013, forthcoming.[4] Bernard Caillaud and Bruno Jullien. Chicken & egg: competition among intermediationservice providers. RAND Journal of Economics, 34(2):309–328, 2003.[5] Yongmin Chen. Paying Customers to Switch. Journal of Economics & ManagementStrategy, 6(4):877–897, 1997.[6] Joseph Farrell and Paul Klemperer. Coordination and Lock-in: Competition withSwitching Costs and Network Effects. In Mark Armstrong and Rob Porter, editors,Handbook of Industrial Organization, volume 3, chapter 31, pages 1967–2072. North-Holland, 2007.[7] Drew Fudenberg and Jean Tirole. Customer poaching and brand switching. RANDJournal of Economics, 31(4):634–657, 2000.23
Page 6: This equation shows that the number
Page 11 and 12: Consider the symmetric equilibrium
Page 13 and 14: 3.4 Switching Costs, One-sided Mark
Page 15 and 16: 3.6 Heterogeneous ConsumersI now tu
Page 17 and 18: Similarly, a side-B consumer is ind
Page 19 and 20: same procedures, and focusing on th
Page 21: AppendicesA Proof of Proposition 3T

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