Caching Games between Content Providers and Internet Service Providers Vaggelis G. Douros Post-Doctoral Researcher, Orange Labs, Paris, France vaggelis.douros@gmail.com Joint work with S.-E. Elayoubi, E. Altman, Y. Hayel ValueTools, Taormina, Italy, 27 October 2016

In a Nutshell Intersection of engineering and economics

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…

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

Baseline Model: The Case of 1 Content Provider

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

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>=0 F: positive constant ISP CP CP Users

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

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

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

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

The Case of Multiple Content Providers

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

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

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

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?

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

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

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

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

Post-Doctoral Researcher, Orange Labs,  Grazie!  Vaggelis G. Douros Post-Doctoral Researcher, Orange Labs, Paris, France vaggelis.douros@gmail.com http://www.aueb.gr/users/douros/

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