Using Two-sided Market Approach. to Analyze the Peer-to-peer Economy 1

Transcription

1 Using Two-sided Market Approach to Analyze the Peer-to-peer Economy 1 Jiangli DOU 2 Abstract In this paper, we use two-sided market approach to analyze how peer-to-peer network works and the end-users behavior in this network Furthermore, we look at the possible policies the network can make in order to overcome the free-riding problem We get the result that when there is some rewards for the sharers while some penalties for free-riders, there will be more sharers and the users welfare increases While if the network compels each of the users to upload at least one file in order to participate in the network, in equilibrium, there will be less users as it prevents the users who do not have an original file out of the network If the network compels the users to provide a minimum proportion of his download, there can be a better result if the minimum amount is not large, there will be more sharers, more users and the users total welfare increases By comparing all of the possible cases, rewarding for sharers is the best one as there will be more incentive for users to upload, compulsory of files is the worst case, it cannot match its original aim to get more available files We also analyze the competition between the peer-to-peer network and an online firm, which can be seen as the standard client-server system If the utility derived from each file is large enough, the firm will not compete with the network, only attracting the users out of the network by setting a price high enough, while if the utility is not very large, the firm will compete with the network and set a lower price But the firm cannot cover the full market even if it sets the price equals to zero 1 I am especially indebted to my supervisor Professor Jacques Cremer for leading me and helping me during the structure of the basic model I further thank Bing YE for conversations and suggestions during the work All of the mistakes are my own 2 TSE and Gremaq Contact information: jldouwhuias@gmailcom 1

2 1 Introduction A Minnesota woman was fined 19 million dollars for illegally downloaded 24 songs from the internet, CNN reported on Friday, June 19, 2009 Before this case, the trial against Jammie Thomas-Rasset was the first case in the United States for the copyright infringement Early to February 12, 2008, there is a piece of news on Times wrote that: People who illegally download films and music will be cut off from the internet under new legislative proposals to be unveiled next week Internet service providers (ISPs) will be legally required to take action against users who access pirated material Users suspected of wrongly downloading films or music will receive a warning for the first offence, a suspension for the second infringement and the termination of their internet contract if caught a third time, under the most likely option to emerge from discussions about the new law Downloading copyrighted files without permission is illegal, it doesn t matter what technology you used to do that, bit Torrent, FTP, web downloads, or getting a CD in the mail However, the technology is legal, bit Torrent is legal, but using bit Torrent or any other technology to download copyright files that you don t have the right is not legal It does not match with the law for copyright protection The peer-to-peer file sharing system has emerged as a significant network for information sharing since the first wide-spread P2P file sharing network, Napster was created in 1999 It was created to allow users to swap music files The subseqent P2P networks, Gnutella was developed by Justin frankel and Tom Pepper in 2000, the Gnutella network was completely decentralized and was difficult to completely shut down through legal means All computers in the Gnutella network were called nodes and when a new node joined the network they were required to find at least one other node Edonkey network was developed in 2000 and began as a centralized P2P architecture FastTrack and Kazaa were developed in March 2001 BitTorrent, the most popular P2P network, account for as much as one third of the internet traffic, was developed in 2002, it used its proprietary protocol called torrent opposed to standard file sharing system such as HTTP and FTP BitTorrent gathered pieces of files simultaneously from several computers in a random order and then reallocated the pieces of files among the searchers computer The advantage was that users could find and download a file at a quicker rate In the peer-to-peer network, files are always transferred directly between the computers of peers connected to the network To this content, the P2P networks share some of the characteristics of public goods and club goods Public goods are goods that have the characteristics of non-excludability in supply and non-rivalry in demand Non-excludability in supply means that individuals can t be excluded from consuming the product In the peer-to-peer network, if the content was provided to one of the users in the network, it should be provided to everyone connect to the network So it satisfied the characteristic of non-excludability in supply Non-rivalry in demand means that one user s consumption of a product does not diminish another user s value of that product In the peer-to-peer network, everyone can download the file and 2

3 derived the same value from consuming the file So it satisfied the characteristic of non-rivalry in demand Club goods are goods that are excludable in supply but non-rival in demand In the peer-to-peer network, if there are so many users connect to the network so it higher the network congestion, each user can only download the file during a longer time In some sense, the files in P2P file sharing network are excludable in supply There are important similarities between the provision of public goods and files in P2P network The individual economic actions will only consider their private utility when making consumption and provision decisions, but will not consider the impact his decision will impose on the others in the network The individual actions in the P2P network may realize to both over consumption and under provision of resources Over consumption may occur because the users may only consider their own utility when deciding their actions of downloading files from the network, but not consider the congestion their actions take to the other users in the network Under provision may occur because the users may only consider their own costs when deciding their actions of sharing files or not, but not consider the benefits their sharing provides to other users in the network Indeed, free-riding is prevalent in existing P2P networks For example, it was estimated by Adar and Huberman (2000) that nearly 70% of Gnutella users did not provide music files In order to incentive the users to provide more files to overcome the free-riding problem, there should be some incentive policy of the network The most prominent two classes of incentive schemes are soft schemes and hard schemes Soft schemes are peer-approved and service-quality Hard schemes, which are monetary based, include token-exchange and micro-payment One of the first studies that considered monetary based schemes in P2P networks is Golle, eyton-brown, Mironov and illibridge (2001) They propose a micro-payment scheme that induces sharing Other papers that examine monetary schemes indlude Ader, Kumar, Ross, Rubenstein, Turner and Yao (2004) Ranganathan, Ripeanu, Sarin and Foster ( 2003 and 2004) were the first to use a game-theoretical approach to study peer-approved and service-quality schemes in the P2P system, they conclude that these schemes provide some incentives for peers to share files Antoniadis, Courcoubetis and Strulo (2005) examined the public good aspect of P2P networks, they find that the equilibrium level of sharing is below the social optimum level and they propose varies of incentive schemes to reduce free-riding problem Whenever the peer-to-peer file sharing technology is legal or not, it has its own mode to work In this paper, we use the two-sided market approach to analyze how peer-to-peer network works and the users behavior in the network, from the comparative statics we can get when there is legal protection for copyright by the government, taxation on the uploaders side is better for prohibiting widespread of pirated copy and protecting copy right We also analyze how the users behavior changes when there are some policies of the network in order to overcome the free-riding problem We get the result that if there are some rewards for sharers while some penalty for free-riders, there will be more sharers than free entry case; if the 3

4 users are compelled to contribute, the equilibrium number of users depends on the value of parameters, the welfare also depends on the parameters If there is an online firm which sells the same product as the peer-to-peer network, it is actual competition between the peer-to-peer network and the standard client-server system We get the result that when the utility each user can derive from each of the file is large enough, the firm will not compete with the peer-to-peer system, but set a very large price only attracting the agents out of the peer-to-peer system; when the utility each user can derive from each of the file is not so large, the firm will compete with the peer-to-peer system and will set a smaller price to attract more agents; but the firm cannot cover all of the market, there are always some users who are better from downloading files in the peer-to-peer network The paper is organized as follows: we explain the similarities and differences between the peer-to-peer network and two-sided market in section 2 In section 3, we setup the basic model to analyze the users behavior in the network In section 4, we analyze the network s policy in order to overcome the free-riding problem In section 5, we compare welfare in different cases In section 6, we analyze the competition between the peer-to-peer network and an online firm Section 7 concludes 2 P2P networks and Multi-sided markets The standard client-server system is composed of two parts; a server, who provides the services and a client, who requests the services There are a lot of standard network functions based on the client-server system, such as exchange, web access Contrary to the standard client-server system, The peer-to-peer network is based on a file sharing protocol which used for transfer files; the peer-to-peer network is a network in which all of the end-users are interconnected to share resources within each other, it initially works when a file owner contributes his original file to the network as the first public resource altruistically so that all of the other users can download what they need from the network In the peer-to-peer network, all of the users simultaneously act as a client and a server Each of the participants in the network is a peer, that why we call it a peer-to-peer network The peer-to-peer file sharing network relies on the computers forming network which allow the transfer of files Each of the peers can search and download what they need from the other computers in the network, yet at the same time they have the ability to provide files to the network so that all of the other peers can download from his computer A file provider can download other files in the network that provide by the others While when downloading files from the network, the user can decide whether to upload the file which he is downloading or not, if he uploads the file at the same time when he downloads, there will be another one available file in the network so that all of the other users can download it evenly, if not, he only gets what he needs from the network without any contribution In the peer-to-peer networks, each peer has two choices of actions; the role of file provider who offering files to other peers and the role of end-user who searching and downloading files from the networks provided by others In order to distinguish these 4

5 two roles of each peer, we call him a file provider when a peer provides files to the network, and we call the file provided by the provider a seed in the network; we call an end-user a sharer when he provides content at the same time when he downloads what he needs from the network, otherwise, we call him a free-rider when he only takes what he needs from the network without any contribution We can define the network an invisible platform by which the end-users can deliver files The peer-to-peer system will starve from resources if every end-user is a free-rider who only takes resources from the system but never contributes There are two effects of a sharer s action: on the one hand, he provides content so that all of the other users can download The user who is sharing does not benefit from the content which he is sharing because he already downloads it from the network, however, he can get some benefit from this altruistic action by contributing to the others in the network On the other hand he supplies upload bandwidth which benefits all the users Of course a sharer should bear some sharing costs which do not exist when free-riding For example, allowing uploads at the same time when downloads may delay his own downloads But for simplicity, we say there is no extension of download time but there is some extra upload cost In the early of 2006, it was estimated that over 10 million users participated in P2P file sharing networks worldwide, more than 10Petabytes of data were available to transfer at any time, which grew very fast from 43 million in September 2003 to 67 million in September 2004 to 93 million in September 2005 Two of the top networks were edonkey and Fast Track, which had five million users each day with a total of 750 million files to transfer For the other P2P networks, Bit Torrent is one of the most common protocols for transferring large files, by some estimates it accounts for about 35 percent of all traffic on the entire internet A growing number of individuals and organizations are using bit Torrent to distribute their own or licensed material Even if Napster no longer operated in the fall of 2002, during its operating period , Napster s software was downloaded 70 million times and from some estimation that 85 percent of collage students in the US were involved with online music swap with Napster When Guntella was developed in 2000, over 20 small companies became Guntella s clients; they developed software based on the Guntella protocol In the P2P network, the download speed depends on the number of peers in the network trying to access a file and the number of peers willing to provide this file, of course it should depend on individual computer processing power and internet connection If we exclude the computers technical problem, the download speed depends on the number of sharers and number of free-riders From our intuition we can see that if there are more users to be sharer in the network, there will be more available seeds in the network so that each of the users can download more in the unit time If there are more users to be free-rider in the network, there will be more users need to download but the number of seeds does not change, so each of the users can download less in the unit time So the number of sharers has a positive effect on the download speed, while the number of free-riders has a negative effect on the download speed, so the number of sharers has a positive externality for both the 5

6 sharers and free-riders, while the number of free-riders has a negative externality for both of them If we divide the users into different groups as what we do for multi-sided market, the peer-to-peer network is an economy with both inter-group externalities and intra-group externalities If we can say there exists an invisible market in this economy which allows the users to interconnect each other and define it as the platform in which the agents in different side interconnect, it is actually a multi-sided market But in the P2P networks, for different definitions of side, there are different sides in the economy If we define all of the users as a side in the economy, it is actually a one-sided market, but there are intra-group externalities within this side If we define the users who download files as one side while the users who upload files as the other side, it is actually a mixed two-sided market for this economy; the free-riders play only on one side of the market, while the sharers play on both sides of the market And the number of sharers has positive externalities for both of the sharers and free-riders, the number of free-riders has negative externalities for both of them If we define the sharers as one side of the market while the free-riders as one side of the market, it is a pure two-sided market, each of the users plays on one side of the market, and there are both inter-group externalities between sharers and free-riders and intra-group externalities between each of the sides However there are some differences between this economy and the standard two-sided market economy The most important one is that the platform only works as a medium in this economy, there is no pricing strategy of the platform so no profit from the users side So we only need to analyze the users behavior 3 The model 31 Setup of the game In reality, there are millions of agents use P2P file sharing systems to deliver files everyday This system has its own mode to work, we intend to analyze the users behavior when participating in the network There are two kinds of participants in this economy Platform: we define there exists an invisible market works as a platform by which the users can deliver files In this economy the platform works only as medium for delivering the files, there is no pricing strategy so no profit from the users side This is different from the standard two-sided market Agents: we assume there are mass 1 of agents in this economy, which can be divided into two groups; of which proportion λ each one has a totally different file which can be delivered by the platform, so they can decide to be a file provider by contributing the file or not We assume each of the files are totally different but with the same type so the users get the same utility by consuming each of the file The other proportion 1 λ of agents does not have an original file to contribute, so they can only download what they need from the platform Each of the agents can decide to be a 6

7 sharer or a free-rider when he participate the platform to download what they need We use pure two-sided market approach to analyze the economy, sharers are on one side of the market and free-riders on the other side of the market The timing of the game is as follows: 1 The proportion λ of agents who has an original file decides to be a file provider or not 2 All of the agents decide to participate in the platform or not, if participate, decide to be a sharer or a free-rider 3 The utility realized For the agent who has an original file: if he provides the file, he can get some utility from the altruistic action that he makes some contribution to the network, but should bear some uploading costs; if he doesn t provide the file, he can get his status-quo utility, which we assume is zero For the user: if a user chooses to be a free-rider, he can get what he needs from the network, of course there is some downloading cost as downloading a file from the network needs some network bandwidth for the user; if he decides to be a sharer, he can get the utility from his altruistic action except for the utility from the file, of course should bear the upload cost except for the download cost 32 Agents utility Agents utility describes the agents preference for different outcomes It depends on the following factors: Satisfaction from downloading the files: Agents can get some utility from consuming the files Altruism or showoff: Agents can derive some self satisfaction from contributing to the operation of the network, which can be explained by satisfaction from altruistic behavior or showoff Downloading time (or speed): Agents care about the time they have to wait for the consumption of the files Bandwidth used: There is a cost associated with the computer when downloading or uploading a file Both download and upload need some network bandwidth and it is a cost for the user as he has to give up some other opportunity to connect to the network Preference of time: Each of the agents has his own opportunity cost or degree of patience of time Now let s calculate the download time for each of the file As we assumed all of the files are with the same type, so they have the same download time Of course the download time depends on the number of feasible content and the available amount 7

8 each one can get Assume the available content (download bandwidth) is shared evenly among the users if there are more than one users connected to a given sharer at the same time So if a user is connected to a sharer at the same time to other k users, this user s expect amount is 1 (1 + k) of the file in each time Obviously the expect amount of a sharer is different from that of a free-rider, as each of the free-rider can connect to all of the sharers in the network, but on the other hand, a sharer can t connect to himself So the expected download time of a sharer should be longer than of a free-rider But in our model, there is infinity number of users so that infinity number of sharers and free-riders, so there is no delay in download time for a sharer We denote the number of sharers by S, the number of free-riders by F The time to download each of the file completely is T if only one user downloads it from the network So for each of the seeds in the network, here are S copies of the file available to download, S + F agents who are intending to access the content (As there are infinity number of users, so we ignore each of the sharers that who contributes the file) So the expected amount of the file each one can get in the unit time is S So the expected time to complete one file is T This is the same as in S Creus Mir, A, Casadeaus-Masanell, R and Hervas-Drane, A (2006) In their setup, there are finite number of sharers and free-riders, both of which are exogenous They get the result that if the amount of files provided in the network could be aggregated and then shared by all users evenly, then each user would obtain the exact same amount in the unit time They show that S is the good approximation to the expected amount when there is finite number of end-users, and the accuracy of this approximation increases with the size of the network So we can get that each of the user obtain an expected download amount S as there are infinity number of users in our network So the expected time to complete download a file is T We can denote γ d and γ u as the associated bandwidth used for download and upload respectively So the expected cost for download and upload a file is Tγ d and Tγ S u respectively For simplicity, we set Tγ d = c d and Tγ u = and denote them by S c d and c S u respectively So we denote the utility function as follows: In the second period, the utility each sharer or free-rider can derive from each file are respectively: U s F + S i = V + θ S i (c d + ) S S 8

9 U i f = V F + S θ S i c d Where V is the utility derived from each of the seed once the download is completed is the benefit from altruism or showoff by contribution θ i is the agent s type, which can be interpreted by the agent s impatience or opportunity cost of time Assume it is uniformly distributed in [0, 1] We can denote c d and as the download cost and upload cost respectively From the formula of the utility function, we can see there are network externalities in this economy The number of sharers has positive externalities to all of the users, not only the sharers but also the free-riders But the number of free-riders has negative externalities to all of the users In the first period, the utility of the agents who have an original file is as follows: U i = θ i, if upload 0, otherwise We assume that V > c d, that is to say, the utility from download the seed is larger than the download cost, so if there is no free-riding problem, all of the agents would like to participate in the platform The second assumption is that >, the altruism can derive from sharing the seed when download is no larger than the upload cost, so not all of the agents would like to be a sharer, there are always some free-riders We can see that in the first period, the utility get from upload only depends on the upload cost, it is nothing to do with the download cost or number of sharers and free-riders 33 Equilibrium Now let s solve the game Each of the users chooses his actions in order to maximize his own utility In the second period, the user with type θ i would like to be a sharer if and only if it is better for him to be a sharer than to be a free-rider That is, iff: V + F + S θ S i (c d + ) V F + S θ S i c d And the participation condition: V + S θ i(c d + ) 0 From the first inequality, we get θ i From the second inequality, we get θ i S S +V c d + Under the assumption V > c d and >, the following condition holds: < +c d c d + +V c d + 9

10 So in equilibrium user i would like to be a sharer if and only if θ i number of sharers is S = S So we can get F + S = S So the Similarly, a user would like to a free-rider if and only if it is better to be a free-rider than to be a sharer That is iff: U f i U s i and U f i 0 By solving these two equations, the condition for free-riders is: S θ i S V c d So: F = S = S V S c d So we have the following result: We can get in equilibrium S = c d 2 If the agents can come to the platform freely, when equilibrium, the number of sharers and free-riders are as follows: S = c d 2 2 V and F + S =, so = V S c d 34 Comparative static analysis and legal protection In reality, the peer-to-peer network is not legal as it hurts the copyright of the creative company If there is legal protection by the government, there should be less participants in the peer-to-peer network The legal protection can both from the uploaders side or the downloaders side Prohibition in the uploaders side has the result of overcome pirated copy for the copyright, while prohibition in the downloaders side has the result of decrease the widespread of pirated copy There are different types of legal protection, for example, the government can put taxation on the users so that increasing the uploading cost or downloading cost, or there can be a positive probability to be fined if the user was monitored by the government From the above result, we can see that if there is taxation or monitor on the uploaders side, the uploading cost will increase, so there will be fewer participants in the network and fewer sharers, and the download time increases While if there is taxation or monitor on the downloaders side, the number of participants does not change while there will be more sharers in the network, so the download time decreases The reason is as follows: if there are penalties on the uploaders side, both the number of providers and sharers decrease, so each of the downloaders can get less file in the unit time, this will drop out some free-riders with the high degree or impatience, the number of free-riders also decreases; if there are penalties on the downloaders side, the uploading cost does not change, so the relative cost of sharers decreases, so there will be more sharers and the download time decreases We can get the result that taxation on the downloaders side increases the number of sharers while decreases the number of free-riders but keep the total number of users unchanged, so it is better for the users The taxation on the downloaders side cannot get the expected result by over-coming the widespread of pirated copy 2 V 10

11 4 Policy of the platform Peer-to-peer file sharing network was first created for users to swap files easily Napster, the first wide-spread P2P file sharing network was created by a 19-year-old Shawn Fanning when he heard complaints from his friend that music was difficult to download from the web The P2P network is efficient if all of the peers are willing to continue making files available after his download has completed If there are all free-riders who only get what they need without any contribution, they P2P network couldn t survive when starve from resources In order for the network play efficiently, there should be some mechanisms when created the technology for P2P systems in order to overcome the free-ride problem We now turn to examine the possible mechanisms the platform implements in order to overcome the free-rider problem The objective of the platform is to encourage users to share resources in the platform or incentive file owners to provide more contents, so that there are more resources and all of the users can get a higher utility We consider the mechanism focuses on penalizing downloads and rewarding uploads For example, we can consider a mechanism that makes use of an internal currency which we call points Users can get points with contribution to the network The more contribution one user make to the network, the more points he can get The points couldn t cash out, so the mechanism must allow the users to maintain a balance from one time period to the next But in this model, we only consider the one period game; there is no need for the rolling balance in our equilibrium However, the users would have no incentive for accumulating more points than they spend if in a repeated equilibrium, so there exist an equilibrium amount of points in the repeated game The more points the user has, the more privilege he can get when participating in the network But in our model, each of the users have at most one file, so the only tradeoff each user faces is to contribute to get the point or not We consider the following policies of the platform: First, the platform gives some rewards for sharing in order to incentive users to share The rewards can be micro payment or non-pecuniary payment The micro payment mechanism can give some money when a user share one file or charge amount of money when download one file Non-pecuniary payment can give some privilege for sharers, for example giving sharers the privilege to download We consider rewarding agents in proportion to the amount of material they make available As in this model, we assume each material gives the same utility to the users, so we can assume that all files have the same size And agents always share files for the same amount of time when they download Each level of sharing in one time period earns one point, with this point the user can get the privilege to download For simplicity, we can assume the sharers have a lower download cost So briefly, assume that the user who shares the material when download can get a lower download cost than original, while the user who free-rides have to wait for the sharers downloading complete and will have a larger download cost The second mechanism in order to have more resources is compelling the users to 11

12 provide files or uploading capacity If the users are compelled to upload files, there is an entry fee; as each user has at most one file in our setup, for simplicity, we assume each user has to upload one unit of material in order to participate in the platform to download the other resources Under this policy, all of the users in the platform have to upload one seed, so there are more choices for the users But the problem is only the agents who have seed can participate in the platform If the users are compelled to provide some uploading capacity, we assume each of them has to contribute at least proportion a of his download so that there are more available seed in the network, and all of the users can participate in the network if they want The last mechanism is combining the first two mechanisms so that the users have more incentive to share and each of the users have to contribute one seed to the platform 41 Rewards for sharing 411 Micro payment We consider micro payment first If there are some payment for sharing while some charge for download, it is the same as the sharers can get a larger but the free-riders can only derive a smaller V From the equilibrium formula, we can see that in equilibrium, there will be more sharers, more participants and the average download time decreases 412 Non-pecuniary rewards If there are some non-pecuniary rewards for the sharers, the sharers can have a smaller download cost while the free-riders have to bear a larger download cost, while the upload cost does not change In this case, the timing of game does not change, the only difference is the utility function in the second period, as follows: U s F + S i = V + θ S i (c d + ) U f F + S " i = V θ S i c d Where c " d > c d > c d can interpret privilege for sharers and penalize for free-riders We keep the similar assumption c d c " d + So that not all of the users would like to share; there are always some free-riders We can get the following result: When there are non-pecuniary rewards for sharing so that the sharers can have a lower download cost, while the free-riders have to bear a larger download cost, we have the following results: If S = " c d V, we have c d + V+ c d " 2 ( c d " +c d ) 2 V and F + S = c " d +c so that = (c " u c d +cd )V d S c " d 12

13 If " c d V, we have c d + V+ S = V+ 2 /( V+ + V c d +c 2 u c d + c " d c " d +c ) and F + S = V+ d c d + In equilibrium, there are more sharers, more participants and the average download time decreases In the first period, there is no change for the agents strategy as the rewards only changes the download cost, nothing to do with the upload cost, so the number of seeds when equilibrium is the same as before 413 Robustness check In our setup of rewards, we simply set the utility derived from altruistic or showoff does not change when the agents know that he can get some rewards from uploading But in the behavioral economics, if people know that they will get some rewards for this behavior, this will decrease his degree of altruism If we can explain this utility by altruism or showoff, there can be different examples to argue this point of view et us consider the following two cases The first example is related to blood donation When the Chinese government encouraged people to donate blood in 1978, there were high compensation and permitting a lot of vacation for this action, but there were not a lot of people would like to donate Most of them are compelled by corporation or government ater on, there was a new law in 1998 and a lot of publicize and advertisement for unpaid blood donation, the proportion of unpaid donated blood in clinical blood usage increases from 22% in 1998 to 955% in 2005 In this example, people s behavior satisfies the standard behavioral economics, people know that there are some rewards for their action, their degree of altruism decreases The second example is agents who like to post in BBS If there are no rewards for posting news or articles in BBS, there are still some agents would like to act this behavior, but if there are some rewards, for example, the agent who posts an article can get more point in BBS or some privilege to read some articles in BBS, there are more users post articles in BBS In this example, users rewarded behavior can get some self satisfaction from showoff, so rewards for this behavior do not decrease this behavior There are a lot of examples to argue this behavior, in our model, for simplicity, we set the users altruistitility does not change even if the users know they can get some rewards If we want to decrease this altruistic behavior in order to satisfy the behavior economy, for example, in the micro-payment case, if we set there is a lower if the users know they can get some rewards for uploading, it is the same as there is a lower micro-payment for uploading and does not change 42 Compelling provide 421 Compulsory of files 13

14 When the users are compelled to provide files, each user has to contribute one file in order to participate in the platform to download resources, only proportion λ of the agents can participate in the network as the others donot have a file to contribute If the agent decides to contribute his file to participate in the platform, he can download all of the other files in the platform As each of the participants has to provide one file, so the total number of files equals to the total number of participants in the platform In this case, it is actually a one period game, the proportion λ of the agents simultaneously decide to be a sharer or a free-rider The utility functions are as follows: U s F + S i = F + S V + θ S i c d + + θ i U f F + S i = F + S V θ S i c d + θ i Now let s solve the game An agent with type θ i decides to be a sharer if and only if: U i s U i f and U i s 0 From F + S V + θ S i c d + + θ i We can get θ i S F + S V F + S θ S i c d + θ i (1) From F + S V + S θ i c d + + θ i 0 We can get θ i V+ + 2 S c d + + (2) If S V+ + 2 c S d + + holds, we can get that F + S = So we need the following condition holds: V 2 c 3 u + Vc d Similarly, an agent decides to be a free-rider if and only if: U f i U s i and U f i 0 We can get the agent decides to be a free-rider if and only if: S θ F + S c i u (F + S)V F + S 2 S c d + We have the following result: 14

15 If the agents are compelled to contribute one file in order to participate in the platform to download resources, we have the following result: If V Vc d, we have S = λ 422 Compulsory of uploading capacity c d 2 2 (V ) and F + S = λ If the users are compelled to provide at least proportion a of his download in order to participate in the network, for simplicity, we assume there is no medium case That is to say, each user will either provide all of that he downloads from the network or only provide proportion a of his download We call the user a sharer if he upload all of that he downloads, and call him a free-rider if he only uploads the minimum amount, that is proportion a of his download In this case there are more available seeds in the network for each of the file As the free-riders have to provide something as well as the sharers But at the same time, this policy hurts the free-riders with large degree of impatience with time as he is not willing to contribute So for the total welfare for all of the users, there is a tradeoff, it depends on which effect dominates The utilities derived from each of the file are as follows: U s F + S i = V + af + S θ i(c d + ) U i f = V + a F + S af + S θ i(c d + a ) Compared with the standard case, the download time decreases from S to a as there are more available seeds The free-riders have to provide proportion a of his download for each of the file, so they can get some altruistitility but have to bear the uploading cost at the same time Agent with type θ i decides to be a sharer if and only if U i s U i f and U i s 0 Solving these two conditions, combined with the assumption V > c d and >, we can get S = a In the free-riders side, the following conditions should hold: U i f U i s and U i f 0 An agent would like to be a free-rider if and only if: a F = a V+a a c d +a So we can get the following two conditions: θ c i a V+a u c d +a So S = a and F + S = a V+a c d +a 15

16 Solving a as a function of F + S and putting it into the formula of S, we can get S = (F + S) c d +a V+a So we can get the following relationship of S and F : 1 c d +a V+a S = c d +a V+a F We set c d +a V+a = m to simplify the calculation from now on So S = get F = m 1 m a+ m 1 m 1+ m 1 m F = a+ m 1 m 1+ m 1 m m 1 m F Putting this condition in the formulation of S, we can So the equilibrium number of free-riders is: 1 m m = ( a + ) (1 m)2 m 1 m m The equilibrium number of sharers is: S = m 1 m F = a + m 1 m 1 m = [a + 1 a m] So F + S = 1 F = a + m 1 m 1 m 1 m m = (a 1 m + 1) m Putting the formula of m into the above equations, we can get S = a + 1 a m = a + 1 a c d +a V+a = a + 1 a 2 (c d +a ) c 2 u (V+a) F + S = a 1 m m + 1 = + a V+a (c d +a ) c d +a 1 m = a m +1 a a 1 m a 1 m we have the following results: m +1 +a+ 1 a m = a V +a (c d +a cu ) +1 c d +acu a 2[ V +a (c d +a )] a c d +a V+a (c d +acu ) V+a +2a If the users are compelled to provide at least proportion a of his download in order to participate in the network In equilibrium, S = a + 1 a 2 (c d +a ), and F + S = + a V+a (c d +a ) c 2 u (V+a) c d +a = (1 a) (c d +a ) V+a +a V+a 2 a 2a(1 a) (c d +a ) V+a +a 2 V+a 2 +(1 a) 2 (c d +a ) 2 From calculation, we can get ln S a = c d + + V a=0 c d V = + V (V c d ) > 0 Vc d ln (F + S) a a=0 = (V c d) > 0 c d From the assumption V > c d and >, we can see that if a is not very large, the 16

17 total number of participants in the network increases as there are more available seeds to download And the number of sharers also increases 5 Welfare analysis In the first stage, the agent who has an original file would like to be a file provider if and only if: θ i 0 That is if and only if: θ i As there are only proportion λ of agents who have original files, so the number of seeds in this network is λ Now let s consider the welfare in this economy As there is no pricing strategy and no profit from the users of the platform, so we only need to consider the users welfare 51 Basic model In the basic case, there is no strategy of the platform, the total welfare includes the utility from consumption of the files and altruistitility deriving from contribution to the network W V = 1 2 W = λ ( λ 2 ( 1 parameters 0 c d 2 c 2 u c 4 u V 2 c d 2 c 2 u V θ )dθ + λ { [ c + (V uv c d θc d)dθ} c d 2 2 V 0 W = 1 2 λ (1 + c d 2 2 c 2 u V + V ) V + V c d θ c d + ]dθ ) which can be positive or negative, depends on the value of We can see that the total welfare increases with λ, and c d, decreases with The total welfare can increase or decrease with V If there are more agents have an original file, the will be a larger welfare; if the altruistitility increases, more agents would like to be sharers or file providers, so the total welfare increases; c d is the relative cost to be a free-rider, so if c d increases or decreases, the relative cost for a free-rider increases, there will be less free-riders, so the total welfare increases 52 Rewards for sharing In the case of micro-payment, it is the same as the sharers can get a larger but the free-riders can only derive a smaller V From the above case, if there are some micro-payments to the sharers while some charge for download, the total welfare may increases or decrease, depending on the value of the parameters In the non-pecuniary case, when c d " c d + V V+, 17

18 c d " 2 ( c d " +c d ) 2 V +λ { [ 0 W R = 1 2 λ [1 + 2 W = λ ( 0 θ )dθ V + ( c " d + c d )V c " θ c d + ]dθ d c + (V ( c " d + c u c " d +c d d )V c " θc d )dθ} c " d 2 d ( c d " +c d ) 2 V 2 2 c d " ( c d " + c d ) 2 V Vc d ( c d " + c d )c d " ] 2 c " d ( c " d + c d ) 3 V + The total welfare increases with λ, and the relative cost for free-riders 53 Compulsory of files If the condition V Vc d holds, the total welfare is: 2V c d " + c d λc d 2 c 2 u V W = {λ [ 0 V + V c d θ c d + ] + θ }dθ λ λcd 2 + {λ V V c d 2 V θc d + θ }dθ W CF = λ2 4 c d c 3 u V c 1 λ 3 4 c d u 2 c 3 u V c + λ2 2 V 1 λ 3 2 V u c 2 u 2 c 2 u The welfare increases with λ, and cost for free-riders + λ2 1 λ Compulsory of uploading capacity If the users are compelled to provide uploading capacity, the uploading cost does not change, so in the first period of the game, the number of seeds is the same as before The total welfare is: W = λ ( θ )dθ

19 a + 1 a 2 (c d +a ) c 2 u (V+a) λ { [ 0 V + +a V+a (c d +a ) c d +a F + S af + S θ c d + ]dθ + [V + a a + 1 a 2 (c d +a ) c 2 u (V+a) F + S af + S θ(c d + a )]dθ} 55 An Example W CU = 1 2 λ + λ [ 1 a S + V + a F + S 2 1 F + S 2 af + S (c d + a ) (F + S) 2 1 a 1 F + S 2 af + S S 2 ] We use an example to analyze the welfare in different cases We set V = 3, = c d = 2, = 1, c d " = 25, c d = 15 and a = 5% From the result in section 3 and section 4, we can get: W = 2 3 λ, WR = λ, WCF = 1 4 λ λ λ, WCU = 07349λ From the analysis in the appendix, we know that if a is not very large, compulsory of uploading capacity is not worse than the basic case By comparing the welfare, we get that the non-pecuniary for sharing is the best from the users point of view, as it gets the highest welfare Compulsory of files is the worst for the users, as it prevents all of the agents who donot have an original file to provide 6 Competition with online firm If there is an online firm offering the same digital files which are also available in the peer-to-peer network, there is competition between them For the firm, in order to persuade users to purchase its product at a positive price, it must offer some added benefits that the P2P network cannot give The most important advantage of the firm is it can offer lower download time than the P2P network We can say the firm can offer the file immediately when you buy We assume there is no cost for the firm So if an user buys the file from the online firm, his utility function is U b = V p Where p is the price set by the firm The timing of the competition game is as follows: 1 The firm sets the price of his product 2 Agents choose either to buy from the firm, or to download from the network, or stay out and not consume the file The agents choose to download in the network decide to be a sharer or a free-rider 3 The agents in the network download the file and utility is realized 19

20 The utility functions for the second period are as follows: U s F + S i = V + θ S i (c d + ) U f F + S i = V θ S i c d U b = V p Now let s solve the game The firm chooses the price in order to maximize his profit From the formula of the utility functions, we know that if an agent with type θ i buys the file from the firm, then all of the agents with type θ j θ i will buy from the firm From the utility function, we can know that if the firm sets p > V, purchasing from the firm yields a negative utility for the user so the firm faces no demand So let s consider the case p V a If the firm sets p = V, only outsiders from the network will buy the good from the firm, as all of the participants in the network can get a positive utility So the demand faced by the firm is 1, the profit of the firm is (1 )V in this case b In order to attract more users to buy its product, the firm should set a lower price From section 3, sharers are the agents with low type while free-riders are the agents with high type If the firm sets lower price in order to attract more consumers, the first agent who deviate from the network going to the platform is a free-rider So if the price is not very low, the low type agents are still sharers in the network while there can be some free-riders buying from the firm In this case, there can be partial sharing in the network or full sharing, if partial sharing, there are both free-riders and sharers If it is full sharing, all of the participants are sharers in the network et s consider the partial sharing case first We denote the agent s type θ i who is indifferent to be a free-rider and to buy from the firm if V F + S θ S i c d = V p So we can get θ i = S p p c d c d So the demand of the firm is 1 S and the profit function is (1 S p c d )p By maximize the profit of the firm, the optimal price for the firm is ()c d 2S and its maximum profit is ()c d 4S Now let s consider the users in the network From the condition of the firm s demand we know that F + S = S p c d Putting p in this equation we can get F + S = 1 2 From the free-rider s participation condition, we know an agent will be a free-rider if and only if: S θ i 1 2 So the number of free-riders is 1 2 S = 1 2 S So if 20

21 the condition 1 2 holds, we can get the result that S = c d The firm s optimal 4V price is V and its profit is 1 V It is the same as what we get in the first case If the 2 condition < 1 2 holds, from section 3 we can get the standard result: S = c d 2 2 V, F + S = the firm s optimal price is p = V 2 and its maximal profit is V 4 c For the smaller p the firm sets, there is no free-riders in the network and it is full sharing case If an agent is indifferent from sharing and buying from the firm, the following condition should be held: V + θ i c d + = V p So we can get θ i = +p c d + The demand faced by the firm is 1 +p c d + and its profit function is (1 +p c d + )p By maximizing the firm s profit function, we get p = c d And its profit in this case is c d c d + d It is not possible for the firm to cover the full market as we should set +p c d + = 0 In this case, we should set a negative price et s consider the user with type θ i = 0, if all of the other agents buy the product form the online firm, the type zero agent would like to be a sharer so that he can get the altruistitility immediately So this agent will not buy from the firm Given that the type zero agent will be a sharer, the other agent with a very low type would like to share in the network So there will always exists some agents participate in the network, the firm cannot cover all of the market So we have the following results: If 1 2 and V 2 c d c d +, the optimal price strategy of the firm is p = V and its maximum profit is π = 1 V The participates in the network are 2 S = c d 4V and F + S = 1 2 If 1 2 and V 2 c d c d +, the optimal price strategy of the firm is p = c d and its maximum profit is π = c d c d + The participates in the network are S = network are sharers 2 c d + In this case, all of peers in the 21

22 If < and V c d c d +, the optimal price strategy of the firm is p = V 2 are S = c d 2, F + S = 2 V and its maximum profit is π = V The participates in the network 4 If < and V c d c d +, the optimal price strategy of the firm is p = c d and its maximum profit is π = c d This 2 2 c d + is the full sharing case and the number of sharers is S = c d + We can see that agents with sufficiently high disutility of time will first deviate from the network to purchase from the online firm The lower the price the firm sets, the more the agents would like to buy from the firm If the firm sets the price low enough, there are only those agents with low disutility of time remain as peers in the network But from section 3, we know that the agents with disutility of time low enough will be sharers in the network, in this case there can be full sharing case in the network All of the other agents with high disutility of time will purchase from the firm As free-riders leave the network, so the sharers utility increases and there will be more sharers in the network If the utility derived from the file V and the relative benefit for uploading are large enough, the firm will not compete with the network and set a high price only attracting the outsiders from the network While if V and are not large enough, the firm prefers to set a lower price in order to attract more consumers to compete with the network Yet the firm can not cover the full market in our model It is because the agents can get some positive utility when uploading 7 Conclusion In this paper we analyze the users behavior in the peer-to-peer network Each user in the peer-to-peer network interconnects with each other in order to transfer files If we can define there exists an invisible market in which the users can deliver files, the peer-to-peer network is actually a multi-sided market The main difference between the peer-to-peer network and the standard two-sided market is there is no price strategy of the platform in the peer-to-peer network We get the equilibrium that the number of sharers increases with the relative cost of free-riders while decreases with the uploading cost We also compare different policies the network can use in order to overcome the free-riding problem There can be rewards for sharers or compulsory of contribution If there are some rewards for sharing, the equilibrium number of sharers and participants increases and the users total welfare increases If the users are compelled to contribute one file in order to participate in the network, the equilibrium number of 22