Differentiated Network Platforms in a Two-Sided Market February 5, 2010 ITA Workshop

Transcription

1 Differentiated Network Platforms in a Two-Sided Market February 5, 2010 ITA Workshop John Musacchio Assistant Professor Technology and Information Management University of California, Santa Cruz johnm@soe.ucsc.edu Dohoon Kim School of Business Kyung Hee University

2 Motivation Content Providers Network Provider Old BE platform New NGN platform Users

3 Questions Content Providers Network Provider BE NGN Users l Suppose NGN users can see BE content but not vice-versa l How will platform selection game play out? l Will Net. Provider price NGN too high for wide adoption? l Ought price differential between NGN and BE be regulated?

4 Background l l l Two sided markets general, including pricing structure issues Rochet and Tirole (2006), Caillaud and Jullien (2003), Chakravorti and Roson (2004), Armstrong (2006), Eisenmannn, Parker and van Alstyne (2006), Parker and van Alstyne (2005) and many others Two sided markets, applied to net-neutrality Economides and Tag (2007) Hermalin and Katz (2006) Hogendorn (2007) Weiser (2007) Musacchio, Schwartz, and Walrand (2009) Njoroge, Ozdaglar, Stier, and Weintraub (2009) Direct network externalities, adoption dynamics Sen, Jin, Guerin, and Hosanagar (2009)

5 Our model in relation to existing work l Key model features Alternative network platforms with monopoly pricing Two sided market Platform selection dynamics, (equilibria, stability) modeled and important to results

6 Model NP simple web pages φ 0 BE CPs (A) α BE Users (A) p A p A δ?? HDTV Movies, interactive Games, NGN CPs (B) β 1 NGN Users (B) p B p B θ 0 simple needs 1 tech-savvy

7 Utility Model The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. BE CPs (A) NGN CPs (B) Utility for User of type θ (1 θ) + αφ m P A Join BE α p A δ β p B θ + α + β(1 φ m ) + δφ m P B Join NGN Utility of CP of type ϕ p A p B (1 φ) + αθ m + δ(1 θ m ) P A Join BE BE Users (A) NGN Users (B) φ + β(1 θ m ) P B Join NGN Players must pick a platform even if both give negative utility Only price difference selection game matters in platform

8 Diffusion Dynamics l Marginal user switches platforms if this increases payoff l Switching rate proportional to the payoff gain $ x = θ m ' & ) % φ m (

9 Platform Selection Game Fixed Prices l Find equilibrium values of x = with fixed price difference Δ l If user of type sees BE platform as more attractive, then BE user population grows

10 Platform selection game analysis l Dynamics on state space boundary

11 Platform selection game analysis l Interior equilibrium: l Stability of eq. depends on eigenvalues being negative. λ 1,2 = 2 ± (α + β δ) l Cross-platform externality parameter δ has stabilizing effect on the interior eq.

12 Extreme Equilibria to Platform Selection Game l (0,0) (All NGN) stable equilibrium iff Δ < β 1 δ l (1,1) (All BE) stable equilibrium iff Δ >1 α + δ l (0,Φ m ) (All Users NGN) stable eq. iff ( 2δ + Δ * β 1 δ, β 1 δ + - ) 2+α+ β δ, l A (θ m,0) type eq. does not exist

13 Network Provider Strategy l Choose price (differential) Δ to maximize revenue l If a Δ leads to multiple stable equilibria, we suppose NP can steer system to more profitable Temporary price breaks to get market to tip toward the equilibrium he wants Focus on best equilibrium with static price for now

14 Technical Detail almost stable equilibrium l Any price strictly below β 1 δ + 2δ 2 + α + β δ (1) l Makes (0,Φ m ) a stable eq. l But Δ=(1) is not stable. l include (1) in maximization because you can get arbitrarily close Like supremum on open set

15 Network Provider Optimal Price l For most α, β, δ, NP s best equilibrium is an extreme eq. in which user market tips CP market splits l Polytope in α, β, δ where an interior point eq. ends up being better:

16 Results Fixed (non-optimal) price α=1, β=3, δ=0 Δ=1 Phase portrait, # set to 1, parameter $= 0 " m, fraction of CPs using BE ALL BE stable (.5,.5) unstable ALL NGN STABLE d! m /dt = 0 d" m /dt = ! m, fraction of users using BE

17 NP Optimizes price " m, fraction of CPs using BE Phase portrait, # set to optimal, parameter $= α=1, β=3, δ=0, Δ= ALL NGN d! m /dt = 0 d" m /dt = ! m, fraction of users using BE

18 NP Optimizes price α=1, β=3, δ=0, Δ=1.99 x 10 3 Close up phase portrait, # set to optimal, parameter $= 0 10 Last graph, zoomed in Phase portrait, # set to optimal, parameter $= 0 " m, fraction of CPs using BE " m, fraction of CPs using BE d! m /dt = 0 d" m /dt = d! m /dt = 0 d" m /dt = ! m, fraction of users using BE ! m, fraction of users using BE x 10 3

19 Varying cross platform network externality Opt. Price vs. Cross Network Externality Constant! 1 Best Equil. vs. Cross Network Externality Constant! Price Premium " Fraction using NGN Cross Network Externality Parameter! 0.2 Users Content Providers Cross Network Externality Parameter! Opt. Revenue vs. Cross Network Externality Constant! Revenue Cross Network Externality Parameter!

20 NP optimizes price δ=1 α=1, β=3, δ=1 Phase portrait, # set to optimal, parameter $= 1 " m, fraction of CPs using BE d! m /dt = 0 d" m /dt = ! m, fraction of users using BE

21 Optimal Transient Price l Consider the objective J = ( 2 [ 1 1]x(t) ) Δ * Δ(t) Δ * (2 [ 1 1]x * )dt 0 l Hamiltonian ( ) # # H = λ T (t) Ax + B + 1 & % % ( Δ * Δ(t) $ $ 1' ( ) & ( + ' ( 2 [ 1 1]x(t) )( Δ * Δ(t) ) Δ * (2 [ 1 1]x * ) l Linear in Δ, optimal control is bang-bang l Provider uses aggressive pricing to get market to tip ASAP.

22 Conclusions l Network provider chooses prices so that market tips to all users using NGN l Suggests that regulating price premium for NGN not necessary to insure wide user adoption Future work l Consider price discrimination between Users and CPs l Alternative utility functions and user distributions