1. Caching Games between Content Providers and Internet Service Providers
Vaggelis G. Douros
Post-Doctoral Researcher, Orange Labs, Paris, France
Joint work with S.-E. Elayoubi, E. Altman, Y. Hayel
ValueTools, Taormina, Italy, October 2016

2. In a Nutshell
Intersection of engineering and economics

3. Motivation (1) Each prisoner wants to minimize his time in prison
Each one spends 5 years…
Do they have motivation to collaborate?
Provide the right incentives…

4. Motivation (2) Prisoner A: Internet Service Provider(s) (ISP)CP
ISP $$ CP
ISP
NO CACHE
CACHE $$
$$$$$ $
$$$$
Prisoner A: Internet Service Provider(s) (ISP)
Prisoner B: Content Provider(s) (CP)
Each ‘prisoner’ wants to maximize his profit
Do they have motivation to collaborate?
Provide the right incentives… through caching

5. Baseline Model: The Case of 1 Content Provider

6. Network economics analysis
Status Quo
ISP CP
Network economics analysis
Content Provider (CP)
Content fee to obtain an item: P
Total demand for the items: D
Profit:
DP-Fixed Expenses
ISP
Access fee: π
Backhaul bandwidth needed for demand D: B
Unit backhaul bandwidth cost: b
Profit: Σπ-Bb
Users
Users pay both access fees and content fees
Bottom line: CP and ISP do not share either their expenses or their incomes

7. The Impact of Caching (1)
ISP deploys a cache of size C for the contents of CP
ISP expenses ↑ 
s: unit cache cost, sC: cost for a cache of size C
ISP Backhaul bandwidth ↓  New bandwidth: Β(1-h), h: hit rate factor in [0,1]
Users Quality-of-Experience (QoE) ↑  Expected demand for CP contents ↑  New demand: (1+Δ)D, Δ=Fh>= F: positive constant
ISP CP CP
Users

8. The Impact of Caching (2)
The profit of the CP with caching is always higher than the profit without caching
The profit of the ISP with caching is higher than the profit without caching iff the backhaul bandwidth savings hBb are larger than the cache cost deployment sC
The question: Do the ISP and the CP have motivation to collaborate?
ISP CP CP
Content Provider (CP)
Content fee to obtain an item: P
Total demand for the items: (1+Δ)D
Profit:
DP +ΔDP -Fixed Expenses
ISP
Access fee: π
Backhaul bandwidth needed for demand D: B(1-h)
Unit backhaul bandwidth cost: b
Profit: Σπ-B(1-h)b-sC
Users

9. Cache Cost/Profit Sharing
We analyze an alternative approach, where the cost/profit due to caching is shared between the CP and the ISP
Φtotal =ΔDP+hBb-sC
We will use coalitional game theory
A coalitional game between the CP and the ISP
How to split Φtotal for a given size C?
Apply the Shapley Value
Appealing due to its fairness properties

10. Shapley Value
Cost/profit due to caching is shared between the CP and the ISP
Φtotal =ΔDP+hBb-sC
A coalitional game between the CP and the ISP
Profit CP: DP-Fixed Expenses+ΦCP
Profit ISP: Σπ-Bb+ΦISP
We prove that:
ΦCP =ΦISP=Φtotal/2= (ΔDP+hBb-sC)/2
Equal cache cost/profit sharing
Same result by applying the Nash Bargaining Solution
ISP CP CP
Users

11. Shapley Value and the Core
In general, the application of the Shapley Value does not lead to a stable outcome 
There are cases where the players have motivation to form a different coalition or to remain selfish
E.g., if the ISP earns 150$ without caching and 100$ with caching
If no player has motivation to leave the coalition, then the outcome is stable and belongs to “the core of the game”
We prove that:
“The Shapley Value belongs to the core of the game if and only if the quantity Φtotal=ΔDP+hBb-sC is non-negative”
Intuition: Cache profit is larger than cache cost

12. The Case of Multiple Content Providers

13. The Straightforward Extension
M CPs
The ISP deploys a cache per CP
Non-overlapping contents
The previous approach is generalized as is 
Network Economics Analysis
CP i
Content fee to obtain an item: Pi
Total demand for the items: Di
Utility:
DiPi-Fixed Expenses
ISP
Access fee per user: π
Backhaul bandwidth needed for CP i: Bi
Unit backhaul bandwidth cost: b
Utility: Σπ-ΣB ib

14. The Case of Overlapping Contents
Caching the contents of CP j has a negative impact on the demand of CP i
New demand: (1+Δi)Di, Δi>=-1
Δi=Fhi-fΣj≠ihj,
F, f: global positive constants
If I do not cache and the others cache, my new demand ↓ 
If all caches offer the same hit rate, there is no change on my demand 
New bandwidth: (1+Θi)Βi (1-hi)
Θi=-fΣj≠ihj>=-1
The more the others cache the lower demand I’ll have I need less backhaul bandwidth

15. Cache Cost/Profit Sharing
We apply again the cache cost/profit sharing scheme
Quantity to be shared per cache:
Shapley Value…
We prove that:
Fair… though ΦCP≠ΦISP

16. A Non-Cooperative Game between the CPs (1)
“Caching the contents of CP j has a negative impact on the demand of CP i”
We should also model this interaction between the CPs
using non-cooperative game theory
Players: The M CPS
Strategy of each player: Choice of the cache size Ci that belongs to the closed interval [0,Ni]
Utility function:
Roadmap
Has the Game a Nash Equilibrium (NE)?
Is the NE unique?
How can we find it/them?

17. A Non-Cooperative Game between the CPs (2)
Has the Game a Nash Equilibrium (NE)?
Yes!
Is the NE unique?
Yes, we prove that:
In that case, we show that the best-response dynamics scheme converges to the unique NE

18. A Non-Cooperative Game between the CPs (3)
Fast convergence to the NE cache size C* for each CP

19. Take-Away Lessons (1) Summary of our contributions
For the case that there is a unique CP:
Fair cache cost/profit sharing between the CP and the ISP using the Shapley Value and the Nash Bargaining Solution
A necessary and sufficient condition for this sharing to be stable, i.e., to belong to the core of the game
Optimal caching policy that maximizes the revenue of both the ISP and the CP

20. Take-Away Lessons (2) Multiple CPs (& overlapping contents):
Fair cache cost/profit sharing between each CP and the ISP using the Shapley Value
Analysis of the non-cooperative game that arises due to the competition among the CPs
This game admits always a NE
Necessary and sufficient condition for the uniqueness of the NE
A best-response dynamics scheme converges fast to the NE

21. Post-Doctoral Researcher, Orange Labs,
 Grazie! 
Vaggelis G. Douros
Post-Doctoral Researcher, Orange Labs,
Paris, France

22. Some Open Issues
How to apply “directly” (part of) this work in the context of Information-Centric Networks?
For the case of multiple CPs
Stability analysis of the sharing mechanism
Optimal caching policy from the ISP side
Network neutrality issues