Contracting Models for P2P Content Distribution

Transcription

1 Contracting Models for P2P Content Distribution Yung-Ming Li Institute of Information Management National Chiao Tung University, Taiwan Nov. 27,

2 Introduction A Peer-to-Peer (P2P) network is a social network for pooling resources such as bandwidth, computing, information, and content File sharing is probably the most successful and prevalent In this paper, we study the contract design of commercial P2P networks

3 P2P market File sharing services would reach $28 billion by 2012 (Insight Research Corporation, 2008) File sharing programs in PC from 51 millions in 2006 to 60.5 million in 2009 (BigCampagne 2009) Snocap uses sound fingerprinting to support song trading over a P2P network Audio Feast use P2P to deliver digital ratio Warner Brothers Home Entertainment use BitTorrent to distribute protected movie and TV program 3 3

4 Realization of Commercial P2P Networks Quality measure (file transfer QoS) Operating policy (provision nodes recommendation) Incentive Mechanism (upload reward and download pricing schemes) 4

5 Quality Measure: File Transfer Delay D: provision delay at peer node T: transmission delay at public network

6 Download Service and Monetary Flow Request Node File swamping Download File request Provision Node Provision Node Provision Node Nodes recommendation P2P Provider Download Compensation Upload Compensation 6

7 Operating Policy of P2P Download 7

8 Optimal effort (upload capacity) Example: Kazza

9 Research Questions P2P service quality problems Uncertain public network Hidden actions problems (moral hazard) on upload capacity provision Optimal contract design Compensation mechanism Pricing scheme Optimal network size QoS maximization Profit maximization Competition of P2P providers

10 The Model 10

11 P2P Dynamics Content Provision x i, m 1, if node i has file F ; m i {1,, n} 0, otherwise, E( x ) : The probability that node i has file F m i, m i, m n : number of active nodes xi,m : Availability of the file Fm stored on node i 11

12 P2P Dynamics Provision Delay (D) The provision delay at peer node j is calculated as D /, where j f0 bjn 1n ˆ p p np f 0 : the size of a file nˆ p : the maximum number of peer node allowed to jointly upload the request file b j : bandwidth capacity 12

13 P2P Dynamics Transmission Delay (T)- delay in the public network Tij : The transmission delay between content request node i and provision node j i.i.d. random variable with density function f(.) uniformly distributed on [0, f 0 τ/n p ] τ : the upper bound of transmission delay per byte 13

14 P2P Dynamics Transfer Delay (denoted as Q) = Provision delay (denoted as D) + Transmission delay (denoted as T) 14

15 P2P Operating Policies Provision policy Recommend the closest (fastest) provision nodes If more than the maximum allowed nodes, n, n can provide a file, only the ranked nodes with topsmallest estimated transfer delay will be selected as the provision nodes. The transfer delay between Q request node i and j Dj Ti, j provision node j is ˆ p ˆ p 15

16 P2P Operating Policies The optimal set of provision nodes j j I I I 1 2 min, ˆ S0 Q j x j, m 1: the set of transfer delay of all satisfied peer nodes S 0 : the total number of satisfied peer nodes S0 n p Ik j Q j inf Sk 1 S S Q j I I I ˆ k1 0 j 1 2 k1 for 2 k np 16

17 Contracting Model The principal (the P2P provider) hires many agents (provision nodes) to perform a task (file upload). The principal cares only on performance (overall transfer delay Q=D+T) and not the effort exerted by agents (upload capacity b or provision delay D). As effort is costly to an agent, the principal has to compensate the agents for incurring this cost. 17

18 Contracting Model Since effort is unobservable, the performance of file transfer is used to evaluate the quality of service. Service price and compensation: w w 0 d : participation compensation : upload compensation p :download price Only the provision node with fastest transfer speed will be chosen to upload the content file, and receives upload compensation!! 18

19 Contracting Model Stages of the contracting game: (1) The P2P provider makes take-it-or-leave-it offers to the peer nodes (2) If they accept the offer, they make the decision of upload bandwidth capacity (4) All contracted peer nodes receive a participation compensation (5) After the content download is completed, the request node pays the P2P provider content download service fee (6) The chosen provision nodes receive the upload compensation 19

20 Optimal Reward Scheme Cost of capacity provision: Assume the cost of bandwidth capacity is c b per byte/sec, the participating cost of peer node i is formulated as C D c b b 0 i b i Reward of uploading service: cf nd ˆ W D w 0 Prob i D is selected w * * i i d p i 20

21 Optimal Reward Scheme The probability that peer node i will be selected as one of the provision nodes nˆ p 1 n 1 Prob i is selected 1 k0 k k i D n1 knˆ n 1 k n 1 k i nˆ p Z k 1 Prob among top- fastest. p Z k 21

22 Optimal Reward Scheme The probability of peer node i being among the top- nˆ p fastest Prob i among top- nˆ fastest Z, T nˆ p 1 u k Dj Tjr Di Tir j J Dj Tjr Di Tir j J Prob, Prob, u0 JG j1 ju1 u nˆ p 1 u k 1 i ir j i ir j u0 JG j1 ju1 u p ir F D T D F D T D 22

23 Optimal Reward Scheme F is the CDF for the transmission delay; therefore, we have: f n p 0 / ˆ ˆ ˆ Prob i among top- n fastest Z Prob i among top- n fastest Z, T f ( T ) dt p p ir ir ir 0 Thus, the probability of being selected as the provision node is determined by endogenous provision delays of all the participating peer nodes and stochastic transmission delay incurred in the public network. 23

24 Optimal Reward Scheme Optimal upload capacity: Solving max D i U W D C D i i i U / D 0 i The optimal provision delay of a peer node i satisfies L( n 1, nˆ ) nˆ w cf0 f D nˆ 0 i * p p d b 2 i n1 n 1 k L( n 1, nˆ p) 1 knˆ k p p, where n 1 k 24

25 Optimal Reward Scheme The best response bandwidth capacity and provision delay of peer node i are: b ˆ * p i cb L( n 1, n ) w * d D f c f * 0 b 0 i * * n? ( 1, )? p L n np wd npbi 25

26 Optimal Reward Scheme Optimal reward scheme Assume that the value of a downloaded content is v. The highest price a peer node is willing to pay is p = v γ ( D+T), where γ represents the sensitivity to delay. 26

27 Optimal Reward Scheme The profit maximization function of the P2P provider max Hp nw w s. t. U 0, w, w 0 d m 0 d i n H 1 1, 1 min, k 1 k n n k n k k nˆ p Solving / D 0 D n nc f H ( n)ˆ n * b 0 p 27

28 Proposition 1. Optimal reward scheme and capacity effort The optimal reward scheme (participation compensation and upload compensation) and capacity effort are given by: W w, w c f H( n) f H( n), f H( n) m* m* b d 2 nn ˆ p n L n n?? p np n L n np np 1, 1, b m * f 0 H( n) n nc nˆ b p 28

29 Corollary 1. The impact of system parameters on the reward scheme and capacity provision n-network size, nˆ p -file swarming, τ-public network, β -content availability, f 0 - content size, c b - bandwidth cost 29

30 The impact of File Swamping Traffic effect Incentive increase Competition effect Incentive decreases 30

31 Optimal Pricing Scheme Service quality: T The expected minimum transmission delay among k nodes is denoted by T min(k). min( k) f0 /min k, nˆ p min kn, ˆ 1 min, ˆ p k k np k! T F( T ) 1 F( T ) f ( T ) dt 0 The expected transmission delay for a file in the network with n nodes T( n) E( T requested file is available) n k 1 k k nˆ ˆ p k np ij ij ij ij ij min,! min, 1! min( k ) n k n k Tmin( k ) (1 ) f0 / H ( n) k 31

32 Corollary 2. The impact of network size, file swarming and content availability on QoS Provision delay increases with network size, whereas transmission delay decreases with network size. Provision delay decreases with the maximum number of simultaneous upload, whereas transmission delay is independent of nˆ p Both provision and transmission delays decrease with expected content availability at each of the nodes. 32

33 Proposition 2. Optimal pricing scheme The optimal pricing scheme of content download service is given by: p * b 0 m ˆ p nc f H( n) n 1H n f0 v H( n) n n 1 H( n) 33

34 Corollary 3. The impact of system parameters on the price scheme and capacity provision 34

35 Optimal Network Size The profit function of P2P provider is rewritten as: H n v 2 nc f H n / nˆ * m b 0 p The P2P quality of service is rewritten as: Q( n) D n T n b 0 H( n) n 1 H( n) f n 1 nc f H( n) n 1 H( n) f0 H( n) nˆ n 1 H n p 0 35

36 Corollary 4. The optimal network size increases with dispersion degree of peer positions. However, the optimal network size decreases with cost of bandwidth capacity. The effect of file size may be positive or negative, depending on cost of bandwidth capacity. 36

37 Optimal Network Size Denote m as the number of satisfied peer nodes for a given content request. We examine the optimal number of provision nodes m who have the requested file and compete for the upload service because the network size can be approximately obtained by calculating n m/. 37

38 Optimal Network Size The profit maximizing function of the P2P provider: m v mc f nˆ f m * max m 2 b 0 / p 0 / 1 m The service quality maximizing function: ˆ min Q m D m T m mc f / n f / m 1 m b 0 p 0 38

39 Proposition 3. Optimal network size Optimal network size that maximizes the profit of the P2P provider is smaller than that * * maximizing service quality. ( m m Q ) When the network size is sufficiently large, approximate optimal numbers of provision nodes are obtained as follows: m? f n / c, m 4 f n / c * 3 2 * p b Q 0 p b 39

40 Competing P2P Networks Two symmetric P2P networks competing for the content distribution service Let m is the total number of P2P participants * that have the requested file, and m the optimal number of satisfied peer nodes in a single P2P network. 40

41 Competing P2P Networks The case of large population of provision * nodes: ( m 2m ) each P2P provider offers the service reward and price schedule at monopolistic level. The reward scheme is built from the participation constraint 41

42 Competing P2P Networks The case of small population of provision * nodes: ( m 2m ) The reward scheme should be built from the incentive constraint as the provider is no longer able extract all the surplus of the participants. In the profit function of a competing P2P provider, we rewrite the objective function as: Dw, ˆ max v D T c f / n D m w c b 0 p c 0 42

43 Proposition 4. Competing P2P networks For a competing P2P networks, the equilibrium reward scheme is: W w, w c* c* 0 d cb f f f nˆ pm m n m 2 c f 2 f c f v m m m n m n *, if m2 m ; * * 2 * ˆ p b 0 0 b 0 * 2 1/ 4 3, 3 if 2. 4 ˆ 2 4ˆ p p b * c 3 f 0 * m ˆ cbn p f 2cn b 0 2 ˆ p * if m 2 m ; * if m 2 m, p * c * m cb f0 f0 * v if m 2 m ; * nˆ p m cb f0 2 f0 * v 3 if m 2 m. nˆ p m 2 43

44 Corollary 5. Upload compensation and capacity provision remain at two constant levels as the population of peer nodes changes. 44

45 Conclusion Utilizing the tournament model from incentive theory, the paper has presented contract (including reward and pricing) scheme for P2P file-sharing networks. We propose a price schedule which is determined based on the performance of P2Pdownload service. 45

46 Summary of Findings QoS issue larger network size, better transmission delay but worse provision delay Optimal Contract Upload compensation increases with uncertainty in public network domain The effect of file swarming technology on upload compensation level is non-monotonic Optimal Network Size Network size of profit maximizing is less than network size of QoS maximization Competitive Market the results are determined by the population of the peer nodes. Upload compensation and capacity provision keep at two different constant levels 46

47 Extended works Heterogeneity of peer nodes Asymmetric Information (adverse selection) Public networks and P2P topology (transmission delay distribution) Comparison of contract formats

48 Research Issues in IT Economics 48

49 Research Issues in IT Economics 49

50 Current Research: IT Monetization Wireless/Mobile Pricing P2P VoIP routing WiFi /MiMax (Hotspot contract, FON ) Web ads Pricing and recommender system Display Ads / Contextual Ads / Keywords Pricing Social Ads delivery Content Pricing DRM pricing Digital movie/music channel Peer production Pricing Platform pricing and planning Market mechanism (YouTube) 50

51 Q & A 51