Game Theory and Pricing of Internet Services Jean Walrand (with Linhai He & John Musacchio)
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Motivation Some users would pay for better network services Fast occasional transfers (sync. databases, backups, …) Videoconferences Streaming of presentations These services are not available A large fraction of infrastructure is poorly used: Wi-Fi access points Why? TOC TOC - Motivation
Jean Walrand – MIT, January 27, Motivation (continued) Bandwidth? QoS Mechanisms? Protocols for requesting/provisioning services? Economic Incentives for providing services are lacking TOC TOC – Motivation
Jean Walrand – MIT, January 27, Motivation (continued) Needed: Economic incentives Billing Mechanism Fair Revenue Sharing among Providers Scalable Correct Incentives Discourage cheating Promote upgrades Revenues Service Quality increases improve TOC TOC Motivation
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Three Problems 1. Service Differentiation Market segmentation Capture willingness to pay more for better services TOC TOC – Three Problems
Jean Walrand – MIT, January 27, Three Problems (cont.) 2. Multiprovider Network Incentives for better services through all providers Improved Services & Revenues TOC TOC – Three Problems
Jean Walrand – MIT, January 27, Three Problems (cont.) 3. Wi-Fi Access Incentives to open private Wi-Fi access points Ubiquitous Access TOC TOC Three Problems
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Service Differentiation Model Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation
Jean Walrand – MIT, January 27, Service Differentiation Model Model Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation
Jean Walrand – MIT, January 27, Model Two possible outcomes: 1.Users occupy different queues (delays = T 1 & T 2 ) 2.Users share the same queue (delay = T 0 ) If users do not randomize their choices, which one will happen? p1p1 p2p2 Users A B H L TOC TOC – Service Differentiation – Model Service Differentiation Each user chooses the service class i that maximizes his/her net benefit
Jean Walrand – MIT, January 27, Model (cont) p1p1 p2p2 A B H L HL B H L A f 1 (T 0 ) – p 2 f 1 (T 1 ) – p 1 f 1 (T 2 ) – p 2 f 1 (T 0 ) – p 1 A’s benefit T 1 < T 0 < T 2 f i (.) nonincreasing TOC TOC – Service Differentiation ModelService Differentiation B’s benefit f 2 (T 0 ) – p 1 f 2 (T 2 ) – p 2 f 2 (T 1 ) – p 1 f 2 (T 0 ) – p 2
Jean Walrand – MIT, January 27, Service Differentiation Model Examples Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation
Jean Walrand – MIT, January 27, Example 1 HL H L B A 9 – 4 = 5 9 – 1 = 8 14 – 4 = 10 5 – 1 = 4 14 – 4 = 10 p1p1 p2p2 A B H L f(T 1 ) = 14 f(T 0 ) = 9 f(T 2 ) = 5 p 1 = 4 p 2 = 1 TOC TOC – Service Differentiation – Examples Service Differentiation Here, f i (.) = f(.)
Jean Walrand – MIT, January 27, Example 1 HL H L B A NE TOC TOC – Service Differentiation – Examples Service Differentiation Assume A picks H. Should B choose H or L? Assume A picks H. Should B choose H or L? Assume A picks H. B should choose H. Assume A picks H. B should choose H. Assume A picks L. Should B choose H or L? Assume A picks L. Should B choose H or L? Assume A picks L. B should choose H. Assume A picks L. B should choose H. B H. Since B chooses H, A should also choose H. NE = Nash Equilibrium
Jean Walrand – MIT, January 27, Example 1 HL H L B A NE TOC TOC – Service Differentiation – Examples Service Differentiation A and B choose H, get rewards equal to 5. If they had both chosen L, their rewards would have been 8! A and B choose H, get rewards equal to 5. If they had both chosen L, their rewards would have been 8! Prisoner’s Dilemma!
Jean Walrand – MIT, January 27, Example 2 HL H L B A 9 – – – – p1p1 p2p2 A B H L T 1 : 13, 11 T 0 : 9, 9 T 2 : 7, 5 p 1 = 4 p 2 = 1 No Pure Equilibrium f 0 f 1 TOC TOC – Service Differentiation – Examples Service Differentiation
Jean Walrand – MIT, January 27, Example 3 Extension to many users Equilibrium exists if 9 0 s.t. willingness to pay total load in class i TOC TOC – Service Differentiation ExamplesService Differentiation (Indeed, ) Also, the other users prefer L. Note: T 1 and T 2 depend on the split of customers. In this equilibrium, users with prefer H.
Jean Walrand – MIT, January 27, Example 3 Analysis of equilibriums: inefficient equilibrium unstable equilibrium Here, f is a concave function and strict-priority scheduling is used. TOC TOC – Service Differentiation ExamplesService Differentiation p1-p2p1-p2 f(T 1 )-f(T 2 )
Jean Walrand – MIT, January 27, Service Differentiation Model Examples Proposal Proposal Joint work with Linhai He TOC TOC – Service Differentiation
Jean Walrand – MIT, January 27, Proposal Dynamic Pricing Fixed delay + dynamic price Provider chooses target delays for both classes Adjust prices based on demand to guarantee the delays Users still choose the class which maximizes their net benefit TOC TOC – Service Differentiation – Proposal Service Differentiation
Jean Walrand – MIT, January 27, Proposal Recommendation: Dynamic Pricing (cont) Why is it better? A Nash equilibrium exists This equilibrium approximates the outcome of a Vickrey auction If an arbitrator knows f i (T 1 ) and f i (T 2 ) from all users, Vickrey auction leads to socially efficient allocation Approximation becomes exact when many users Simpler to implement TOC TOC Service Differentiation – ProposalService Differentiation
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Multiprovider Network Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Multiprovider Network Model Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network
Jean Walrand – MIT, January 27, Multiprovider Network Model Model Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network
Jean Walrand – MIT, January 27, Model + p 1 + p 2 p1+ p2p1+ p2 Monitor marks and processes inter- network billing info Pricing per packet TOC TOC – Multiprovider Network ModelMultiprovider Network
Jean Walrand – MIT, January 27, Multiprovider Network Model Nash Game Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network
Jean Walrand – MIT, January 27, Nash Game: Formulation 12 p1p1 p2p2 D Demand = d(p 1 +p 2 ) C1C1 C2C2 A game between two providers Different solution concepts may apply, depend on actual implementation Nash game mostly suited for large networks Provider 1 Provider 2 TOC TOC – Multiprovider Network – Nash Game Multiprovider Network
Jean Walrand – MIT, January 27, Nash Game: Result 1. Bottleneck providers get more share of revenue than others 2. Bottleneck providers may not have incentive to upgrade 3. Efficiency decreases quickly as network size gets larger (revenues/provider drop with size) TOC TOC – Multiprovider Network Nash GameMultiprovider Network
Jean Walrand – MIT, January 27, Multiprovider Network Model Nash Game Revenue Sharing Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network
Jean Walrand – MIT, January 27, Revenue Sharing Improving the game Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network
Jean Walrand – MIT, January 27, Revenue Sharing Improving the game Improving the game Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network
Jean Walrand – MIT, January 27, Revenue Sharing - Improving the Game Possible Alternatives Centralized allocation Cooperative games Mechanism design Our approach: design a protocol which overcomes drawbacks of non-cooperative pricing is in providers’ best interest to follow is suitable for scalable implementation TOC TOC – Multiprovider Network – Revenue Sharing ImprovingMultiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing Improving the game Model Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network
Jean Walrand – MIT, January 27, Revenue Sharing - Model Providers agree to share the revenue equally, but still choose their prices independently 1 2 p1p1 p2p2 D Demand = d(p 1 +p 2 ) C1C1 C2C2 Provider 1 Provider 2 TOC TOC – Multiprovider Network – Revenue Sharing ModelMultiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing Improving the game Model Optimal Prices Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices # of providers Lagrange multiplier on link i “locally optimal” total price for the route sum of prices charged by other providers A system of equations on prices TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) For any feasible set of i, there is a unique solution: On the link i with the largest , * ), p i * = N * + g( p i * ) On all other links, p j * = 0 Only the most congested link on a route sets its total price TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) {i}{i} {pi*}{pi*} {dr*}{dr*} a Nash game with i as the strategy It can be shown that a Nash equilibrium exists in this game. Each provider solves its i based on local constraints TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) Comparison with social welfare maximization (TCP) Social: Sharing: Incentive to upgrade Upgrade will always increase bottleneck providers’ revenue A tradeoff between efficiency and fairness TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) Efficient when capacities are adequate It is the same as that in centralized allocation Revenue per provider strictly dominates that in Nash game TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) A local algorithm for computing i that can be shown to converge to Nash equilibrium: TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing - Optimal Prices (cont.) 1 i d hop count N r =0 congestion price r =0 flows on route r N r =N r +1 r = max( r, i ) A possible scheme for distributed implementation … … … No state info needs to be kept by transit providers. TOC TOC – Multiprovider Network – Revenue Sharing OptimalMultiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Revenue Sharing Improving the game Model Optimal Prices Example Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network
Jean Walrand – MIT, January 27, Example C 1 =2 C 2 =5 C 3 =3 demand = 10 exp(-p 2 ) on all routes r1r1 r2r2 r3r3 r4r4 ii link 1 link 3 link 2 prices p2p2 p3p3 p1p1 p4p4 TOC TOC Multiprovider Network – Revenue Sharing – ExampleMultiprovider Network Revenue Sharing
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Wi-Fi Pricing Conclusions References TOC
Jean Walrand – MIT, January 27, Wi-Fi Pricing Motivation Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio
Jean Walrand – MIT, January 27, Wi-Fi Pricing Motivation Motivation Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio
Jean Walrand – MIT, January 27, Motivation Path to Universal WiFi Access Massive Deployment of base stations for private LANs Payment scheme might incentivize base station owners to allow public access. Direct Payments Avoid third party involvement. Transactions need to be “self enforcing” Payments: Pay as you go: In time slot n, - Base Station proposes price p n - Client either accepts or walks away What are good strategies? TOC TOC – Wi-Fi Pricing MotivationWi-Fi Pricing
Jean Walrand – MIT, January 27, Wi-Fi Pricing Motivation Web-Browsing Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio
Jean Walrand – MIT, January 27, Web Browsing Client Utility U = Utility per unit time K = Intended duration of connection Random variable in [0, 1] Known to client, not to BS Random variable in {1, 2, …} Known to client, not to BS BS Utility p 1 + p 2 + … + p N U.min{K, N} N = duration TOC TOC – Wi-Fi Pricing – Web Browsing Wi-Fi Pricing
Jean Walrand – MIT, January 27, Web Browsing Theorem Perfect Bayesian Equilibrium: Client accepts to pay p as long as p ≤ U BS chooses p n = p* = arg max p p P(U ≥ p) Note: Surprising because BS learns about U … TOC TOC – Wi-Fi Pricing Web BrowsingWi-Fi Pricing
Jean Walrand – MIT, January 27, Wi-Fi Pricing Motivation Web-Browsing File Transfer File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio
Jean Walrand – MIT, January 27, File Transfer Client Utility K.1{K ≤ N} BS Utility p 1 + p 2 + … + p N K = Intended duration of connection Random variable in {1, 2, …} Known to client, not to BS N = duration TOC TOC – Wi-Fi Pricing – File Transfer Wi-Fi Pricing
Jean Walrand – MIT, January 27, File Transfer Theorem Perfect Bayesian Equilibrium: Client accepts to pay 0 at time n < K p ≤ K at time n = K BS chooses a one-time-only payment pay n* at time n* = arg max n nP(K = n) Note: True for bounded K. Proof by backward induction. Unfortunate …. TOC TOC – Wi-Fi Pricing – File Transfer Wi-Fi Pricing
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions Conclusions References TOC
Jean Walrand – MIT, January 27, Conclusions Dynamic Pricing to adjust QoS Cooperative pricing -> distributed algorithm Web browsing -> constant price File transfer -> one-time price TOC TOC – Conclusions
Jean Walrand – MIT, January 27, Conclusions Basic objective Improve revenues by better mechanisms for - service differentiation - pricing - revenue sharing Some preliminary ideas New pricing schemes - rational (equilibrium) - desirable incentives - implementable (scalable protocols) TOC TOC Conclusions
Jean Walrand – MIT, January 27, Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References References TOC
Jean Walrand – MIT, January 27, References TOC TOC References Linhai He and Jean Walrand, "Pricing Differentiated Internet Services," INFOCOM 2005 Linhai He and Jean Walrand, "Pricing and Revenue Sharing Strategies for Internet Service Providers," INFOCOM 2005 John Musacchio and Jean Walrand, "Game-Theoretic Analysis of Wi-Fi Pricing," IEEE Trans. Networking, 2005
Jean Walrand – MIT, January 27, Thank you!