1. The Role of Switching Hub in Global Internet Traffic Chang-Ho Yoon Young-Woong Song Byoung Heon Jun

2. Introduction Internet traffic is growing fast. Connection between networks becomes important. Popular contents generates internet traffic. The role of switching hub becomes less important as regionalization of Internet traffic gains speed. Persistent asymmetry in bargaining power was a serious policy issue in late 1990s due to global digital divide, which shows changes only recently. This paper examines the role and the bargaining power of the switching hub, taking into account the above listed facts.

3. Findings Bargaining power of the local networks depends on the quality adjusted volume of net traffic (the difference between the outbound and inbound traffic weighted by the quality). Rent to the hub depends on total traffic between the local networks connected to the switching hub. When there is competition, capacity constraint destroys most of the rent for the constrained hub and offers more rent for the rival. This creates a tendency for excess capacity. Peering possibility reduces the rent of the hub.

4. Literature Shapley (1953), “A Value for n-Person Games”, in Kuhn and Tucker eds., Contributions to the Theory of Games II Laffont, Marcus, Rey, and Tirole (2001), “Internet Interconnection and the Off-Net-Cost Pricing Principle”, mimeo, Institut d’Economie Industrielle Milgrom, Mitchell, and Srinagesh (2000), “Competitive Effects of Internet Peering Policies”, in Compaine and Vogelsang eds., The Internet Upheaval Besen, Milgrom, Mitchell, and Srinagesh (2001), “Advances in Routing Technologies and Internet Peering Agreements”, AEA Papers and Proceedings

5. Model Networks are denoted by i  I. Each network hosts one contents provider CP i, and serves n i identical consumers. –Alternatively, we can assume perfect competition in each content market. A consumer in each network has a separable utility function; –u i (q,y)=  j ( j q j – q j 2 /(2 ij )) + y From the utility function of the consumers demand function for j is derived Q j (p j ; j )= iS n i  ij ( j – p j ), where –S is the set of networks connected to j, – ij represents the preference of consumer i for contents j, – j represents popularity or “quality” of content j.

6. Preliminary results Contents price; p j ( j ) =  j /2 Consumer’s surplus; CS ij =  ij  j 2 /8 Network operators charge prices so as to extract all the consumers’ surplus. Network i’s profit when connected to S TS i S =  jS n i  ij  j 2 /8 One can calculate Shapley value using this information. Shapley value determines the actual payoff of each network, and payments by each network is the difference between the total profit and the Shapley value.

7. Premium for the hub Proposition 1. The payment of the transit purchaser consists of two parts. The first part is proportional to the quality adjusted net inbound traffic. The second part is proportional to the quality adjusted total traffic between the non-hub networks. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 )]/8 + ( 2  21 +  1  12 )/24 NP 2 = [( 1  12 –  2  21 ) + ( 3  32 –  2  23 )]/8 + ( 2  21 +  1  12 )/24 NP 3 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 )]/8 – ( 2  21 +  1  12 )/12 (Hub)

8. Competition of hubs Proposition 2. When there are two hubs, the premium payments are reduced to half the level when there is only one hub, and each hub receives one quarter of the premium received when there is only one hub. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 ) + ( 4  41 –  1  14 )]/8 + ( 2  21 +  1  12 )/48 (transit purchaser) NP 3 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 ) + ( 4  43 –  3  34 )]/8 – ( 2  21 +  1  12 )/48 (hub)

9. Collusion If the two hubs collude and act as a monopolist, then they collectively obtain the same premium that can be obtained when there is only one hub. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 ) + ( 4  41 –  1  14 )]/8 + ( 2  21 +  1  12 )/24 (transit purchaser)

10. Capacity constraint * Now suppose that each hub can only host one transit purchaser. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 ) + ( 4  41 –  1  14 )]/8 + ( 1  12 +  2  21 )/16 + [( 1  13 +  3  31 ) + ( 1  14 +  4  41 )]/48 NP 3 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 ) + ( 4  43 –  3  34 )]/8 – ( 1  12 +  2  21 )/16 – [( 1  14 +  4  41 ) + ( 2  24 +  4  42 )]/48 + [( 1  13 +  3  31 ) + ( 2  23 +  3  32 ) – ( 1  14 +  4  41 ) – ( 2  24 +  4  42 )]/96

11. Partial constraint * Now suppose that only network 4 has capacity constraint in the sense it can host only one transit purchaser. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 ) + ( 4  41 –  1  14 )]/8 + ( 1  12 +  2  21 )/24 + ( 1  14 +  4  41 )/48 NP 3 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 ) + ( 4  43 –  3  34 )]/8 – ( 1  12 +  2  21 )/12 – [( 1  14 +  4  41 ) + ( 2  24 +  4  42 )]/32 (hub with no constraint)

12. Partial constraint * NP 4 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 ) + ( 3  34 –  4  43 )]/8 + [( 1  14 +  4  41 ) + ( 2  24 +  4  42 )]/96 (“hub” with constraint) NP 4 = [( 1  13 –  3  31 ) + ( 2  23 –  3  32 ) + ( 3  34 –  4  43 )]/8 + [( 1  14 +  4  41 ) + ( 2  24 +  4  42 )]/24 (transit purchaser)

13. Investment game Hub 4 Do not invest Invest Hub 3 Do not invest ++, ++–, +++ Invest+++, –+, +

14. Possibility of peering Proposition 3. If peering generates more benefit to the interconnecting networks than the construction cost, the premium to the hub network is reduced. The smaller is the peering cost, the smaller the premium becomes. There will be no premium if peering is costless. NP 1 = [( 2  21 –  1  12 ) + ( 3  31 –  1  13 )]/8 + min{( 2  21 +  1  12 )/24, F/6} (F = cost of peering)