Wireless Network Pricing Chapter 7: Network Externalities Jianwei Huang & Lin Gao Network Communications and Economics Lab (NCEL) Information Engineering Department The Chinese University of Hong Kong Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 1 / 46
The Book E-Book freely downloadable from NCEL website: http: //ncel.ie.cuhk.edu.hk/content/wireless-network-pricing Physical book available for purchase from Morgan & Claypool ( http://goo.gl/JFGlai ) and Amazon ( http://goo.gl/JQKaEq ) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 2 / 46
Chapter 7: Network Externalities Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 3 / 46
Section 7.1: Theory: Network Externalities Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 4 / 46
What is Externality? Definition (Externality) An externality is any side effect (benefit or cost) that is imposed by the actions of a player on a third-party not directly involved. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 5 / 46
Examples: Negative Externality Air Pollution (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 6 / 46
Examples: Negative Externality Second-hand Smoke (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 6 / 46
Examples: Negative Externality Traffic Congestion (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 6 / 46
Examples: Positive Externality Lighthouse (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 7 / 46
Examples: Positive Externality Bee Keeping (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 7 / 46
Examples: Positive Externality Immunization (source: Internet) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 7 / 46
Impact of Externality Can cause market failure without proper prices ◮ The market outcome will no longer be efficient. ◮ If market prices do not reflect the costs or benefits of externalities. Example: negative externality of pollution ◮ The market price for steel reflects the cost labor, capital, and other inputs, but may not include the cost due to air pollution. ◮ The steel manufacturer may produce more products than the socially optimal level. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 8 / 46
Graphical Illustration of Market Failure Price Price MC(social) MC MR(external) MC(external) MC(private) MR(social) MR(private) MR Q ∗ Q ∗ 0 Q 1 Quantity 0 Q 1 Quantity Social optimal production level Q ∗ : ◮ Social Marginal Cost (MC) = Social Marginal Revenue (MR) Left: negative production externality ◮ Private MC < Social MC ◮ Local optimal quality Q 1 > Social optimal quality Q ∗ Right: positive consumption externality ◮ Private MR < Social MR ◮ Local optimal quality Q 1 < Social optimal quality Q ∗ Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 9 / 46
Negative Network Externality Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 10 / 46
A Case Study: Water Pollution The chemical company produces chemical products and discharges wastewater into the river. The water company produces bottle water by drawing water from the river. Water pollution increases the production cost of the water company. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 11 / 46
Graphical Illustration Price MC(social) MC(private) MC(external) D $10 MR E A B F C Q ∗ 0 Q 1 Quantity Constant MR per chemical product: $10. Social MC = private MC (chemical plant) + external MC (pollution) Social optimal quant Q ∗ < local optimal quality Q 1 Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 12 / 46
At Local Optimal Quality Q 1 Price MC(social) MC(private) MC(external) D $10 MR E A B F C Q ∗ 0 Quantity Q 1 The chemical plant’s profit (i.e., revenue - cost): � Q 1 ( MR − MCPrivate ( Q )) d Q = A + B + E 0 The water company’s profit due to externality (assuming 0 revenue): � Q 1 − MCExternal ( Q ) d Q = − ( C + F ) 0 Since C = B and F = D + E , the social surplus (sum of two profits): A + B + E − ( C + F ) = A − D Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 13 / 46
At Social Optimal Quality Q ∗ Price MC(social) MC(private) MC(external) D $10 MR E A B F C Q ∗ 0 Quantity Q 1 The chemical plant’s profit (i.e., revenue - cost): � Q ∗ ( MR − MCPrivate ( Q )) d Q = A + B 0 The water company’s profit due to externality (assuming 0 revenue): � Q ∗ − MCExternal ( Q ) d Q = − C 0 Since C = B , the social surplus (sum of two profits): A + B − C = A Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 14 / 46
Comparison Social suplus at Q 1 : A − D Social surplus at Q ∗ : A With negative externally, individual profit maximization hurts the social surplus Solution: Pigovian tax Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 15 / 46
Pigovian Tax MC(social) Price MC(private)+Tax MC(private) MC(external) $10 MR A 1 A 2 B Tax C Q ∗ 0 Q 1 Quantity Charge chemical plant a tax ◮ Tax = external marginal cost at the optimal solution Q ∗ Individual profit maximisation leads to production level of Q ∗ � Q ∗ ◮ Chemical plant profit = ( MR − MCPrivate ( Q ) − Tax ) d Q = A 1 0 Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 16 / 46
The Coase Theorem Nobel Laureate Ronald Coase proposes another view of externality Assumptions: Transaction cost is negligible, property rights are clear Result: Trade in externality will lead to efficient use of the resource Back to the previous example ◮ If water company owns the water: it can charge the chemical plant a price equal to the negative externally ◮ If chemical plant owns the water: it can demand a compensation from water company for reducing the chemical production quantity ◮ Either way, it is possible to maximize social surplus Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 17 / 46
Positive Network Externality Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 18 / 46
A Case Study: Network Effect More usage of the product by any user increases the product’s value for other users. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 19 / 46
Metcalfe’s Law Consider a network of N users. Each user perceives a value increasing in N . Each user attaches the same value to the possibility of connecting with any one of the other N − 1 users. Total network value N ( N − 1) ≈ N 2 . Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 20 / 46
Briscore’s Refinement Each user ranks other users in terms of decreasing importance. Attach a value of 1 / k to the k th important neighbour. �� N − 1 � 1 Total network value N ≈ N log N . k =1 k Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 21 / 46
Different Types of Network Effect Direct network effect: telephone, online social network Indirect network effect: Office for Windows, DVDs for DVD players Local network effect: instant messaging Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 22 / 46
Section 7.2: Distributed Wireless Interference Compensation Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 23 / 46
Wireless Power Control Distributed power control in wireless ad hoc networks Elastic applications with no SINR targets Want to maximize the total network performance Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 24 / 46
Network Model T 2 h 1 12 h 2 12 R 1 h 1 h 2 11 R 2 11 T 1 T 3 R 3 Single-hop transmissions. A user = a transmitter/receiver pair. Transmit over one or multiple parallel channels. Interferences in the same channel (negative externality). Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 25 / 46
Single Channel Communications σ 1 Transmitters Receivers p 1 h 11 h h 2 1 12 σ 2 p 2 h 22 σ M p M We focus on a single channel. For each user n ∈ N = { 1 , ..., N } : ◮ Power constraint: p n ∈ [ P min , P max ]. n n ◮ Received SINR (signal-to-interference plus noise ratio): p n h n , n γ n = . σ n + � m � = n p m h n , m ◮ Utility function U n ( γ n ): increasing, differentiable, strictly concave. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 7 November 20, 2018 26 / 46
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