1. To Whom the Revenue Goes: A Network Economic Analysis of the Price War in the Wireless Telecommunication Industry
Vaggelis G. Douros, Petri Mähönen  
Institute for Networked Systems,
RWTH Aachen University, Germany
TPRC45, September 8, Arlington, VA

2. Motivation (1)
Price war
How does the producer set the price?

3. Motivation (2)
How does the consumer choose among the brands?

4. Contributions
We analyze the ongoing price war in the telecommunications industry under the prism of network economics
Case study:
2 Mobile Service Providers (MSPs), N End-users

5. How a User Selects a MSP? (1)
We take into account two parameters:
Price P of each MSP
Reputation R of each MSP
R1>R2
P1<P2 user will choose MSP1
P1>P2 ?
R1<R2
P1<P2 ?
P1>P2 user will choose MSP2
How to quantify the importance of each parameter?
How the user compares the values of the same parameter for the different MSPs?

6. How a User Selects a MSP? (2)
We introduce a weighted metric:
w1=aR1/(R1+R2) + (1-a)P2/(P1+P2) for MSP1
Weight coefficient a in [0,1] & w1 is in [0,1]
w2=1-w1 for MSP2
If w1 >1/2 user will choose MSP1
If w1 <1/2 user will choose MSP2
A user may choose a MSP independent of the price of the other MSP

7. How a MSP Sets his Price?
Given the price of MSP2, which is the maximum price that MSP1 should choose in order to get a particular user?
The case that the MSP sets the minimum possible price is trivial
Which is the target of the MSP?
Market Share Maximization
Profit Maximization
Revenue Maximization

8. Market Share Maximization
Each user can be considered as a 0/1 quantity
when the MSP gets one user, it increases by 1 his market share
Case study: 1 user
w1=aR1/(R1+R2) + (1-a)P2/(P1+P2) for MSP1
Let P⎔ be the max. price so that w1>1/2
3 cases:
P⎔ =PmaxMSP1 can get the user by setting the max. price
P⎔ belongs to [Pmin,Pmax)
Impossible for the MSP1 to get the user, even by setting the price to Pmin

9. Market Share Maximization (2)
How to generalize for the case that we have N users?
Typical assumption: the MSP should set a unique price
MSP1  computes the price P⎔ per user n 
among those users that he can attract them, he chooses the min. price

10. Revenue Maximization (1)
How the MSP charges the user?
Volume-based pricing scheme
Revenue per user: Demand of the user x unit price
Users do not contribute equally to the revenue
Flat-rate pricing scheme
Revenue per user: Fixed subscription fee
The decision between the two models takes into consideration the cost
 fixed marginal cost to add a user
a variable cost that increases with his data consumption

11. Revenue Maximization (2)
Flat-rate pricing model:
The price that maximizes the revenue coincides with the price that maximizes the market share
Why?
Volume-based pricing model:
For the case of one user, the price that maximizes the revenue coincides with the price that maximizes the market share
For 2+ users, the prices are different
The MSP computes the max. price to serve each user
The max. revenue among these prices corresponds to the requested price

12. Numerical Example

13. Market Share of MSP1 as a Function of his Price
Market share is a decreasing function of the price
Even by setting the min. price, the MSP cannot attract some users
Even by setting the max. price, the MSP will get some users
In the regulatory domain: how much there is true differentiation possibilities between MSPs

14.  Sum of the Data Consumption of the Users that Choose MSP1 as a Function of his Price
The shape of the curve is similar to the one of the market share
The market share of a higher price is a subset of the market share of a lower price
We assume that the demand is inelastic for the price range that we study

15. Revenue of MSP1 as a Function of his Price (1)

16. Revenue of MSP1 as a Function of his Price (2)
 Revenue is not a monotonic function of price
Revenue is a function of both price and demand
When market share is pretty high, it is close to 0 == the revenue of MSP1  is very low
When the MSP sets his price too high, his revenue is low
Rule of thumb for a coarse-grained analysis of the price strategy
Choose a price level high enough but lower than the price of the competitor
You get all the users that prefer you in terms of reputation
You might get some of the other users

17. Discussion (1)
Open issue: a quantitative evaluation of flat-rate pricing model vs. volume-based pricing model
We can even study more schemes such as cap-based pricing where the MSP charges a fixed fee up to a point and if the user exceeds this cap, there is an additional charge per unit of volume
Is it rational for MSPs to offer all three pricing plans simultaneously?

18. Discussion (2)
Revisiting our assumption that  the MSPs announce their prices sequentially
significant advantage of the MSP who announces second his pricing policy
but this process can be iterative: what if the second MSP decides to update his pricing policy?
 Though our analysis holds for any particular step, we cannot predict the outcome after a number of steps, can’t we?
Game theory is the right tool to analyze this problem, as well as its variation where the MSPs announce (and update) their prices simultaneously

19. Take-home Messages
The key regulatory and techno-economical conclusions are two-fold:
 price discrimination may yield significantly different market share/revenue
though these targets demand different pricing policies, given the pricing policy of one MSP, there is a correlation between the market share and the revenue of the other MSP

20.  Thanks!  Dr. Vaggelis G. Douros Institute for Networked Systems,
RWTH Aachen University, Germany
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