1. Caching Games between Content Providers and Internet Service Providers
Vaggelis G. Douros
Joint work with S.-E. Elayoubi, E. Altman, Y. Hayel
LINCS Seminar, 12 October 2016

2. My Ph.D. Research Word Cloud (AUEB, Athens, Greece)

3. My Post-Doctoral Research Word Cloud (Orange Labs & LINCS)
Intersection of engineering and economics

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

5. 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

6. Baseline Model: The Case of 1 Content Provider

7. 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
Utility (Profit):
DP-Fixed Expenses
ISP
Access fee: π
Backhaul bandwidth needed for demand D: B
Unit backhaul bandwidth cost: b
Utility: 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

8. 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
Backhaul bandwidth ↓  New bandwidth: Β(1-h), h: hit rate factor in [0,1]
Users QoE ↑ => Expected demand for CP contents ↑  New demand: (1+Δ)D, Δ=Fh>= F: positive constant
ISP CP CP
Users

9. The Impact of Caching (2)
New CP Utility: Always higher than the utility without caching
New ISP Utility: Higher than the utility 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
Utility (Profit):
DP +ΔDP -Fixed Expenses
ISP
Access fee: π
Backhaul bandwidth needed for demand D: B(1-h)
Unit backhaul bandwidth cost: b
Utility: Σπ-B(1-h)b-sC
Users

10. Cache Cost/Profit Sharing
We analyze an alternative approach, where cost/profit due to caching is shared between the CP and the ISP
Φtotal =ΔDP+hBb-sC
We will use game theory to analyze it…
Why?
“I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.” A. Moslow, The law of the instrument, 1966 ;)
The ISP and the CP should decide between the following two strategies:
Sharing, No sharing
Game theory is a powerful tool to model these interactions

11. Why Game Theory? John F. Nash Competition=non- cooperative game theory
Nobel Econ. 1994
Competition=non- cooperative game theory
Status quo ~ Nash Equilibrium
Lloyd Shapley
Nobel Econ. 2012
Cooperation= coalitional game theory
Our approach ~ Shapley Value

12. Shapley Value
Cost/profit due to caching is shared between the CP and the ISP
Φtotal =ΔDP+hBb-sC
A coalition game between the CP and the ISP
How to split this quantity for a given size C?
Apply the Shapley Value
Appealing due to its fairness properties
Utility CP: DP-Fixed Expenses+ΦCP
Utility 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

13. Shapley Value and the Core
In general, 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

14. Optimal Caching Policy (1)
How to split this quantity for a given size C?
How to determine the cache size C?
Which will be the optimal cache size C*?
If the ISP controls the cache size: maximize UISPmaximize ΦISP = (ΔDP+hBb-sC)/2
If the CP controls the cache size: maximize UCPmaximize ΦCP = (ΔDP+hBb-sC)/2
We need an explicit formula for the hit rate h
We use the approximation of Elayoubi &
the N items of the CP are of equal size
their popularities follow a Zipf(a) distribution, a: Zipf parameter in (0,1)
the number of items N is large

15. Optimal Caching Policy (2)
We prove that the optimal cache size C* follows the form
This result is independent of who controls the cache size

16. The Case of Multiple Content Providers

17. 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

18. 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 constants
If I do not cache and the others cache, the new demand decreases
New bandwidth: (1+Θi)Βi (1-hi)
Θi=-fΣj≠ihj>=-1
Bandwidth reduces linearly with the sum of the other hit factors

19. Cache Cost/Profit Sharing
We apply again the cache cost/profit sharing scheme
Quantity to be shared per cache:
Shapley Value…
We prove that:

20. 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 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 reach at it/them?

21. 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

22. A Non-Cooperative Game between the CPs (3)
Average number of iterations needed so that the best-response dynamics scheme converges to the unique NE. Fast convergence to the NE

23. 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

24. Take-Away Lessons (2) Multiple CPs (& overlapping contents):
Fair cache cost/profit sharing between each CP and the ISP using the Shapley
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

25. 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

26. References
V.G. Douros, S.-E. Elayoubi, E. Altman, Y. Hayel, “Caching Games between Content Providers and Internet Service Providers,” Proc. 10th EAI International Conference on Performance Evaluation Methodologies and Tools (Valuetools), Taormina, Italy, October Candidate for the best paper award.
The full version of the paper has been selected to be published in the Elsevier Performance Evaluation (PEVA) Journal.

27. Please join my “pot de départ”… after the Q&A part ;)
 Merci! 
Please join my “pot de départ”… after the Q&A part ;)
Vaggelis G. Douros