Caching Games between Content
Providers and Internet Service
Providers
Vaggelis G. Douros
Post-Doctoral Researcher, Orange Labs, Paris, France
[email protected]
Joint work with S.-E. Elayoubi, E. Altman, Y. Hayel
ValueTools, Taormina, Italy,
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27 October 2016
In a Nutshell
Intersection of engineering and economics
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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…
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Motivation (2)
CP
CP
NO CACHE
CACHE
ISP
NO CACHE
ISP
$$
CP
$$
ISP
$$$$$
CP
$
CACHE
ISP
$
CP
$$$$$
ISP
$$$$
CP
$$$$
 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
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Baseline Model: The Case of 1
Content Provider
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Status Quo
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
CP
ISP
Users
Users pay both access fees and content fees
Bottom line: CP and ISP do not share either their
expenses
or their incomes
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The Impact of Caching (1)
CP
ISP
Users
CP
 ISP deploys a cache of size C for the
contents of CP
1. ISP expenses ↑ 
s: unit cache cost,
sC: cost for a cache of size C
2. ISP Backhaul bandwidth ↓ 
New bandwidth: Β(1-h), h: hit rate factor
in [0,1]
3. Users Quality-of-Experience (QoE) ↑ 
Expected demand for CP contents ↑ 
New demand: (1+Δ)D, Δ=Fh>=0
F: positive constant
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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?
CP
ISP
Users
CP
Content Provider (CP)
Content fee to obtain an
item: P
Total demand for the
items: (1+Δ)D
Profit:
DP +ΔDP -Fixed
Expenses
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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
8
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
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Shapley Value
 Cost/profit due to caching is shared between the
CP and the ISP
CP
ISP
Users
– Φtotal =ΔDP+hBb-sC
CP
 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
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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
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The Case of Multiple Content
Providers
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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
ISP
Content fee to obtain
Access fee per user: π
an item: Pi
Backhaul bandwidth
Total demand for the
needed for CP i: Bi
items: Di
Unit backhaul
Utility:
bandwidth cost: b
DiPi-Fixed Expenses
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Utility: Σπ-ΣB ib
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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
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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
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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?
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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
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A Non-Cooperative Game
between the CPs (3)
 Fast convergence to the NE cache size C* for
each CP
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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
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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
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 Grazie! 
Vaggelis G. Douros
Post-Doctoral Researcher, Orange Labs,
Paris, France
[email protected]
http://www.aueb.gr/users/douros/
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21
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
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