230 A.A. Sofokleous and M.C. Angelides Fig. 4 The Main Game Phase: Round 2 may decide to decline an offer if the offer was not good enough or if he can wait for the next game to get a better offer. The former is calculated from the objectives and constraints set by the player whereas the latter is the payoff of the game to players that give up their bandwidth during a game. The server will take into account their decision and in the next game these players will get at a better offer. Before moving to the next round, all the players must make their initial YES or NO decision. The result of this round is that some players (i.e. with a YES decision) will satisfied in terms of bandwidth, whereas some other will have to wait. 10 Dealing Bandwidth to Mobile Clients Using Games 231 Round 2 - remainder bandwidth dealing (RBD): this round will go ahead only if there is enough bandwidth to satisfy at least one more player (Figure 4). For exam- ple, consider the case where the last player declined the server’s offer. In figure 4, player 1, who decided last in round 1, declined the offer of server. If b 1 , which is the bandwidth offered to player 1, is also the available bandwidth at the end of round 1, in round 2 the objective is to use this bandwidth to make a new offer to the unsatis- fied players. Following a vice-versa order, i.e. FIFO on the initial settlement of the gameQueue players, the server offers this bandwidth to each one of each one of the players that declined its offers earlier. If one of the players takes the offer then this round terminates and the game proceeds to the next phase. At the end of round 2, the server satisfies the players who accepted the offer, e.g. in figure 4 player k  1 accepted the offer. Players, who have not gone with any of the server’s offers, e.g. in figure players k and 1, will play again in the next game and not get any bandwidth from the current game. Streaming-Seat Reallocation Phase Figure 5 shows the final phase of the game, where players are either served, if they accepted an offer, or change seat in order to participate in the next game. The new seat arrangement is one of the payoffs of the players who have decided to wait, e.g. player k in Figure 5. In addition, the fact that the server will make a better offer to those players is another payoff of waiting to be served in future games. For example, if the current game is game t, and player j is a player of game t waiting to be served in the next game, then b j .t C 1/ D b j .t/ C e , where e is a small additional amount of bandwidth given to these players, e.g. e D . Bb j .t/ / k . Concluding Discussion This paper describes a game approach to dealing bandwidth. It proposes the model- ing of bandwidth allocation based on five-card poker draw, where players are users awaiting to be served sufficient bandwidth. Each player participates in the game under a number of rules for gaining the wanted bandwidth resources. Players have priorities according to the time of arrival. One of the difference of our approach is that it takes into account the length of the queue and the time that a player may need to wait before getting served. Thus, in some cases, the players can sacrifice the quality of the video in order to be served faster, or may choose to wait more in exchange of getting more bandwidth. We are currently extending our algorithm to incorporate content adaptation. 232 A.A. Sofokleous and M.C. Angelides Fig. 5 The Streaming-Seat Reallocation Phase 10 Dealing Bandwidth to Mobile Clients Using Games 233 References 1. H. Agius and M. C. Angelides, “Closing the content-user gap in MPEG-7: the hanging basket model,” Multimedia Systems, Vol. 13, No. 2, 2007, pp. 155-172. 2. D. Andrei, M. Batayneh, S. Sarkar, C. U. Martel and B. Mukherjee, “Deadline-driven band- width allocation with flexible transmission rates in WDM networks,” Proceedings of the IEEE International Conference on Communications (ICC’08), Beijing, China, 2008, pp. 5354-5358. 3. M. C. Angelides, A. A. Sofokleous and M. Parmar, “Classified ranking of semantic content filtered output using self-organizing neural networks,” Lecture Notes in Computer Science 4132: Proceedings of the 16th International Conference on Artificial Neural Networks (ICANN 2006) Part II, Athens, Greece, 2006, pp. 55-64. 4. M. C. Angelides, A. A. Sofokleous and C. Schizas, “Implementing the MPEG-21 adapta- tion quality of service in dynamic environments,” Lecture Notes in Computer Science 3983: Proceedings of the 2006 IEE International Conference on Computational Science and its Ap- plications (ICCSA2006) Part IV, Glasgow, UK, 2006, pp. 118-127. 5. H. Boche, M. Wiczanowski and S. Stanczak, “On Optimal Resource Allocation in Cellular Networks With Best-Effort Traffic,” Wireless Communications, IEEE Transactions on, Vo l . 7 , No. 4, 2008, pp. 1163-1167. 6. J. Chakareski and P. Frossard, “Rate-Distortion Optimized Distributed Packet Scheduling of Multiple Video Streams over Shared Communication Resources,” IEEE Transactions on Mul- timedia, Vol. 8, No. 2, 2006, pp. 207-218. 7. S. L. Chao, G. Y. Lin and H. Y. Wei, “Mixed altruistic and selfish users in wireless mesh net- works: A game theoretic model for multihop bandwidth sharing,” Proceedings of the 9th ACM International Symposium on Mobile Ad Hoc Networking and Computing, 2008, pp. 461-462. 8. N. Cranley, P. Perry and L. Murphy, “Optimum adaptation trajectories for streamed multime- dia,” Multimedia Systems, Vol. 10, No. 5, 2005, pp. 392-401. 9. A. Creus-Mir, R. Casadesus-Masanell and A. Hervas-Drane, “Bandwidth allocation in peer- to-peer file sharing networks,” Computer Communications, Vol. 31, No. 2, 2008, pp. 257-265. 10. E. Del Re, G. Gorni, L. S. Ronga and M. A. Vazquez Castro, “A game theory approach for DVB-RCS resource allocation,” Proceedings of the IEEE 67th Vehicular Technology Confer- ence (VTC’08), Singapore, 2008, pp. 2937-2941. 11. A. H. Elghirani, R. Subrata and A. Y. Zomaya, “A proactive non-cooperative game-theoretic framework for data replication in data grids,” Proceedings of the 8th IEEE International Sym- posium on Cluster Computing and the Grid (CCGRID’08), Lyon, France, 2008, pp. 433-440. 12. J. Elias, F. Martignon, A. Capone and G. Pujolle, “A new approach to dynamic bandwidth allocation in Quality of Service networks: Performance and bounds,” Computer Networks, Vol. 51, No. 10, 2007, pp. 2833-2853. 13. Z. Fang and B. Bensaou, “Fair bandwidth sharing algorithms based on game theory frame- works for wireless ad-hoc networks,” Proceedings of the 23th Conference of the IEEE Communications Society (INFOCOM’04), Hong Kong, 2004, pp. 1284-1295. 14. N. Feng, S. C. Mau and N. B. Mandayam, “Pricing and Power Control for Joint Network- Centric and User-Centric Radio Resource Management,” IEEE Transactions on Communica- tions, Vol. 52, No. 9, 2004, pp. 1547. 15. D. Fotakis, S. Kontogiannis, E. Koutsoupias, M. Mavronicolas and P. Spirakis. “The structure and complexity of nash equilibria for a selfish routing game,” Theoretical Computer Science, 2008, available online from http://dx.doi.org/10.1016/j.tcs.2008.01.004. 16. M. Gruhne, R. Tous, J. Delgado, M. Doeller and H. Kosch, “MP7QF: An MPEG-7 query for- mat,” Proceedings of the 3rd International Conference on Automated Production of Cross Media Content for Multi-Channel Distribution, (AXMEDIS’07), Barcelona, Spain, 2007, pp. 15-18. 234 A.A. Sofokleous and M.C. Angelides 17. P. Guturu, “Computational intelligence in multimedia networking and communications: Trends and future directions,” in Computational Intelligence in Multimedia Processing: Recent Advances, vol. 96/2008, A. Hassanien, A. Abraham and J. Kacprzyk, Eds. Springer Berlin / Heidelberg, 2008, pp. 51-76. 18. J. L. Hsiao, H. P. Hung and M. S. Chen, “Versatile Transcoding Proxy for Internet Content Adaptation,” IEEE Transactions on Multimedia, Vol. 10, No. 4, 2008, pp. 646-658. 19. D. Jannach, K. Leopold, C. Timmerer and H. Hellwagner, “A knowledge-based framework for multimedia adaptation,” Applied Intelligence, Vol. 24, No. 2, 2006, pp. 109-125. 20. Z. Ji and K. J. R. Liu, “Dynamic Spectrum Sharing: A Game Theoretical Overview,” IEEE Communications Magazine, Vol. 45, No. 5, 2007, pp. 88. 21. S. Kalasapur, M. Kumar and B. Shirazi, “Personalized service composition for ubiquitous multimedia delivery,” Proceedings of the 6th IEEE-CS International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM’05), Taormina, Giardini, Naxos, 2005, pp. 258-263. 22. H. Kung, J. Hua, Y. Chang and C. Lin, “Seamless QoS Adaptation Control for Embedded Multimedia Communications,” IEEE Transactions on Consumer Electronics, Vol. 52, No. 1, 2006, pp. 240-248. 23. R. T. B. Ma, S. C. M. Lee, J. C. S. Lui and D. K. Y. Yau, “A game theoretic approach to provide incentive and service differentiation in P2P networks,” Proceedings of the Joint International Conference on Measurement and Modeling of Computer Systems, 2004, pp. 189-198. 24. R. T. B. Ma, S. C. M. Lee, J. C. S. Lui and D. K. Y. Yau, “Incentive and service differentiation in P2P networks: a game theoretic approach,” IEEE/ACM Transactions on Networking (TON), Vol. 14, No. 5, 2006, pp. 978-991. 25. R. T. Maheswaran and T. Basar, “Multi-user flow control as a nash game: Performance of var- ious algorithms,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, 1998, pp. 1090-1095. 26. J. M. Mart´ınez, “MPEG-7 Tools for Universal Multimedia Access,” Journal of the American Society for Information Science and Technology, Vol. 58, No. 9, 2007, pp. 1374-1376. 27. F. Meshkati, H. V. Poor and S. C. Schwartz, “Energy-efficient resource allocation in wireless networks: An overview of game-theoretic approaches,” IEEE Signal Processing Magazine, Vol. 24, 2007, pp. 58-68. 28. D. Mukherjee, E. Delfosse, J. Kim and Y. Wang, “Optimal Adaptation Decision-Taking for Terminal and Network Quality-of-Service,” IEEE Transactions on Multimedia, Vo l . 7 , N o . 3 , 2005, pp. 454-462. 29. M. J. Neely, E. Modiano and C. Li, “Fairness and Optimal Stochastic Control for Heteroge- neous Networks,” IEEE/ACM Transactions on Networking, Vol. 16, No. 2, 2008, pp. 396-409. 30. W. Ogryczak, A. Wierzbicki and M. Milewski, “A multi-criteria approach to fair and efficient bandwidth allocation,” Omega, Vol. 36, No. 3, 2008, pp. 451-463. 31. M. Prangl, T. Szkaliczki and H. Hellwagner, “A Framework for Utility-Based Multimedia Adaptation,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 17, No. 6, 2007, pp. 719-728. 32. P. Ranganathan, E. Geelhoed, M. Manahan and K. Nicholas, “Energy-Aware User Interfaces and Energy-Adaptive Displays,” IEEE Computer, Vol. 39, No. 3, 2006, pp. 31-38. 33. A. Sahasrabudhe and K. Kar, “Bandwidth allocation games under budget and access con- straints,” Proceedings of the 42nd Annual Conference on Information Sciences and Systems (CISS’08), Princeton, NJ, 2008, pp. 761-769. 34. A. A. Sofokleous and M. C. Angelides, “Client-Centric Usage Environment Adaptation using MPEG-21,” Journal of Mobile Multimedia, Vol. 2, No. 4, 2006, pp. 297-310. 35. A. A. Sofokleous and M. C. Angelides, “Content Adaptation on Mobile Devices using MPEG- 21,” Journal of Mobile Multimedia, Vol. 2, No. 2, 2006, pp. 112-123. 36. A. A. Sofokleous and M. C. Angelides, “DCAF: An MPEG-21 Dynamic Content Adaptation Framework,” Multimedia Tools and Applications, Vol. 40, No. 2, 2008, pp. 151-182. 10 Dealing Bandwidth to Mobile Clients Using Games 235 37. A. A. Sofokleous and M. C. Angelides. “Dynamic selection of a video content adaptation strategy from a pareto front,” The Computer Journal, 2008, available online from http://dx. doi.org/10.1093/comjnl/bxn035. 38. P. J. Teller and S. R. Seelam, “Insights into Providing Dynamic Adaptation of Operating Sys- tem Policies,” ACM SIGOPS Operating Systems Review, Vol. 40, No. 2, 2006, pp. 83-89. 39. B. Veeravalli, L. Chen, H. Y. Kwoon, G. K. Whee, S. Y. Lai, L. P. Hian and H. C. Chow, “Design, analysis, and implementation of an agent driven pull-based distributed video-on- demand system,” Multimedia Tools and Applications, Vol. 28, No. 1, 2006, pp. 89-118. 40. A. Vetro, C. Timmerer and S. Devillers, “Digital item adaptation - tools for universal multime- dia access,” in The MPEG-21 Book I. S. Burnett, F. Pereira, R. Van de Walle and R. Koenen, Eds. Hoboken, NJ, USA: John Wiley, 2006, pp. 282-331. 41. A. Vetro and C. Timmerer, “Digital Item Adaptation: Overview of Standardization and Re- search Activities,” IEEE Transactions on Multimedia, Vol. 7, No. 3, 2005, pp. 418-426. 42. F. Yu, Q. Zhang, W. Zhu and Y. Q. Zhang, “QoS-adaptive proxy caching for multimedia streaming over the Internet,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 13, No. 3, 2003, pp. 257-269. Chapter 11 Hack-proof Synchronization Protocol for Multi-player Online Games Yeung Siu Fung and John C.S. Lui Introduction Modern multi-player online games are popular and attractive because they provide a sense of virtual world experience to users: players can interact with each other on the Internet but perceive a local area network responsiveness. To make this possible, most modern multi-player online games use similar networking architecture that aims to hide the effects of network latency, packet loss, and high variance of delay from players. Because real-time interactivity is a crucial feature from a player’s point of view, any delay perceived by a player can affect his/her performance [16]. Therefore, the game client must be able to run and accept new user commands continuously regardless of the condition of the underlying communication channel, and that it will not stop responding because of waiting for update packets from other players. To make this possible, multi-player online games typically use protocols based on “dead-reckoning” [5, 6, 9] which allows loose synchronization between players. However, dead-reckoning protocol is susceptible to some security attack or exploitation. In particular, the type of cheat that exploits this vulnerability is called speed-hack [3] and it has become so widely available and easily accessible because the implementation of a speed-hack is very simple. Speed-hack cheats exist virtually in all popular commercial multi-player online games [15]. Existing countermeasures target on the cheats themselves, i.e. they scan for and block any known cheating software, or observe any abnormal network traffic and ban that player from the game. These methods cannot safeguard against all potential speed-hacks, and honest players may be accidentally recognized as cheaters due to the false positive nature of detection software. Figure 1a and b are screenshots from a popular commercial massively mul- tiplayer online role-playing game (MMORPG) called World of Warcraft.Inan Y.S. Fung and J.C.S. Lui (  ) Department of Computer Science and Engineering, The Chinese University of Hong Kong, Ma Liu Shui, China e-mail: fsfyeung; csluig@cse.cuhk.edu.hk B. Furht (ed.), Handbook of Multimedia for Digital Entertainment and Arts, DOI 10.1007/978-0-387-89024-1 11, c Springer Science+Business Media, LLC 2009 237 238 Y.S. Fung and J.C.S. Lui Fig. 1 a Some avatars moving inside a virtual world, each of them is controlled by an individual player. b Several avatars attacking each other using different weapons MMORPG, each player controls the action of an avatar inside a virtual world. For example, the player can move the avatar from one place to another, gather different items by moving the avatar towards them, use different weapons and magic spells to attack other avatars and move the avatar to avoid being attacked. Therefore, a player with a fast moving avatar has definite advantages over players with slower moving avatars. Normally, an avatar can move faster only after it has obtained some partic- ular items. However, when using speed-hack an avatar can move arbitrarily faster. Figure 4 illustrates the effect of using speed-hack in an MMORPG. In Fig. 4c and d, player P is using a speed-hack. We can see that P’s avatar moves faster than that in Fig. 4a and b. This paper presents a novel dead-reckoning protocol that is immune from the speed-hack cheats. We assume the cheater can modify any binary code or game data, e.g. the OS’s clock speed, the memory data, the incoming and outgoing packets, etc. However, we will prove that the invulnerability of our protocol does not depend on what the cheater can do and even the cheater can modify the outgoing packets, only very limited advantages can be gained. Since our protocol is based on the conven- tional dead-reckoning protocol, existing games can easily be modified to become resistant to speed-hack. Our protocol can be adapted to both client-server architec- ture and P2P architecture in a very similar way. Backgrounds Dead-reckoning In most multi-player online games, before the game starts, a player is able to select among a number of avatars, each having different abilities and characteristics, such as appearance, health point, magic point, speed, etc. When the game begins, or when 11 Hack-proof Synchronization Protocol for Multi-player Online Games 239 a player joins an existing game session, the avatar will be given an initial speeding capability. This speeding capability may be different according to which avatar the player has chosen. This speeding capability limits how fast the avatar can move in the virtual world. The avatar can be moving or stationary at any moment during the game, but while it is moving, its speed is fixed. Throughout this paper, we call this speed the legal speed of the avatar. The legal speed of the avatar can be changed when the game is in progress. It can be achieved by either gaining enough experience points to upgrade the avatar’s abilities or by obtaining special items which will affect the avatar’s abilities. In a client-server architecture, the change of an avatar’s legal speed needs to be granted by the game server and the game server will broadcast the new legal speed of that avatar to all clients. In a peer-to-peer architecture, the change of an avatar’s legal speed needs to be verified by all peers. For example, all peers must agree that the avatar has obtained the specific item successfully and so they will update its legal speed accordingly. Therefore, the change of the legal speed of an avatar works under a tight synchronization requirement. Synchronization protocols based on dead-reckoning are commonly used in multiplayer online games because they do not require synchronization at every state change. In a game using dead-reckoning, each client sends update packet to the server (in client-server architecture) or to the peers (in peer-to-peer architec- ture) at a constant interval called timeframe, instead of at each state change. An update packet consists of a timestamp of the game states and a dead-reckoning vector while a dead-reckoning vector consists of the current coordinates and mov- ing direction of the avatar. Using the latest received update packet, each client can predict the movement of another player before the next packet arrives. When a new packet arrives, correction will be made if there is any deviation induced by the prediction. Therefore, players do not maintain strictly synchronized views at every state change. Instead, their views will only be re-synchronized each time when the synchronization takes place. An important advantage of this loose synchronization is that the rate of graphics rendering at each client side can be made independent to the rate of synchronization. In order to produce smooth display, the graphics should be rendered at a rate no less than 30 frames per seconds (fps). However, synchronization in MMORPGs typically takes place in a much slower rate. This is because synchronization can consume a significant amount of processing power and network bandwidth the server since the number of connected clients are typically in the order of thousands. The situation is even more severe in peer-to-peer games, since IP multicast is still not yet widely available, a peer-to-peer game client may resort to sending separate update packets to every peer. Because of this, synchronizations in MMORPGs typically take place at a rate less than 10 updates per second, i.e. a timeframe of 100 ms. If a client only renders moving objects to their new coordinates each time when an update packet arrives, i.e. it renders the graphics at a rate of 10 fps, the animation will look choppy and jittery, which will definitely destroy the game’s playability. However, under dead-reckoning, since prediction is carried out before any newer packet is available, each client can render the movement of objects at the fastest rate which only depends on the processing power of the client machine. 240 Y.S. Fung and J.C.S. Lui In order to predict an object’s movement from its previous game states, simple linear extrapolation can be used. Using the dead-reckoning vector in the last received packet, the client can extrapolate a linear movement from the object’s last known coordinates which head towards the last known direction. When a new update packet arrives, the accurate coordinates may be different from the current coordinates pre- dicted by the extrapolation. Algorithms such as [1] and [11] can be used to hide the effect of any extrapolation error emerged in rendering the movements. Under the dead-reckoning protocol with the use of extrapolation, all clients can render the movement of all avatars at the fastest possible rate, which only depends on the com- putational power of the client side. If an update packet is late on arrival or is even lost, the graphics rendering will still not be affected and therefore smooth gameplay can be ensured. Linear Extrapolation We give an example to illustrate a simple linear extrapolation algorithm. Referring to Fig. 2, when a client sends an update packet at time t 1 , it is reported that avatar P is at .x 1 ;y 1 / heading at an angle r. Before the next synchronization scheduled at time t 2 occurs, other clients render P’s movement by linearly extrapolating the position of P based on P’s dead-reckoning vector sent at time t 1 , as follows: x.t/ D x 1 C.t  t 1 /  legal speed of P  sin.r/ y.t/ D y 1 C .t  t 1 /  legal speed of P  cos.r/  for t  t 1 time t t (x , y ) (x , y ) (x, y) t t sm005sm005 dead-reckoning vector r 0 0 21 11 0 Fig. 2 Extrapolation of .x; y/ from the latest dead-reckoning vector [...]... with circled tails Only some of the dead-reckoning vectors are displayed on the figures for a clear view of the paths Figures 15 and 16 zoom into the last 60 s of Figs 13 and 14 respectively We can see that the clients are still synchronized correctly after 10 min of simulation Speed-hacking on a client is achieved with generic over-clocking software together with a spoofed NTP source However, doing... the exchange of location information requires four parameters: x-coordinate, y-coordinate, angle, and the timestamp Typically, a game divides the whole map into smaller areas called zones Assuming a two-bytes integer is used for a single coordinate, a floating point number for the angle in radian, and a double precision timestamp, the total payload for the location information is therefore 2 C 2 C 4... prevention system for commercial online games HLGuard [20], formerly called CSGuard, is a free server-side anticheat system for a famous commercial FPS game, Half-Life, and many variations of Half-Life Besides PunkBuster and HLGuard, there are a few other commercial anti-cheating software [21] Basically, they are pattern scanners that scan for known cheats in the client machine The anti-cheating software must... completely prevented and these anti-cheating software themselves are also vulnerable to hacks In [2], the authors describe a type of cheat called suppress-correct cheat and propose a cheat-proof protocol that resists this type of cheat Suppose a cheater S uses the suppress-correct cheat and S purposefully drops n packets while receiving n packets from each of other players, other players will be forced to extrapolate... R1 ; R2 and the timestamp requires four double precision numbers implies a total of 32 bytes Since 25 frame-per-second or above is enough for a fluent video display, we assume 25 synchronizations per second (in practical 5–10 is usually enough) concurrently 11 Hack-proof Synchronization Protocol for Multi-player Online Games 259 Fig 14 The path of the local avatar Q (thicker line) and the path of the... protocol to handle these cases Scenario 1 Referring to Fig 12, suppose player P has moved and stopped occasionally, or has accelerated and decelerated occasionally, between time tn and tnC1 so that the total length of the path P taken is shorter than the maximum possible displacement if P moves continuously with its legal speed We re-define the value of d for a greater generality: d D legal speed of P elapsed... latency and the theorem 11 Hack-proof Synchronization Protocol for Multi-player Online Games 257 Implementation We have implemented a prototype server and a prototype client to demonstrate the feasibility of our proposed protocol The prototype server only acts as a broadcaster which forwards dead-reckoning packets to all clients The prototype client automatically generates random moves continuously and. .. elapsed time Therefore, when the host of P computes its synchronization parameters and when the server (or the peers) computes P’s new coordinates from the 11 Hack-proof Synchronization Protocol for Multi-player Online Games 255 R S avator’s motion path, not moving at full speed R2 R1 M tn tn+1 time Fig 12 Player P has stopped or decelerated occasionally between time tn and tnC1 , therefore the path MR... time, too Therefore, the illegal overall displacement is bounded by illegal overall displacement Ä legal speed of P latency tn 1 /g f.t1 t0 / C t2 t1 / C : : : C tn C single-trip Dlegal speed of P tn C single-trip latency t0 / Dlegal speed of P tn t0 / C legal speed of P single-trip latency Dlegal displacement C legal speed of P single-trip latency/ The extra displacement is legal speed of P is hence... Figure 4a and b illustrate the views of two interacting honest players P and Q respectively In the figures, P’s avatar is moving upward while Q’s avatar stays motionless P sends two updates at time tn and tnC1 respectively, giving Q the information to render the two opaque avatars corresponding to P’s position at time tn and tnC1 respectively However, when rendering P’s position between time tn and tnC1 . (  ) Department of Computer Science and Engineering, The Chinese University of Hong Kong, Ma Liu Shui, China e-mail: fsfyeung; csluig@cse.cuhk.edu.hk B. Furht (ed.), Handbook of Multimedia for Digital Entertainment. initial settlement of the gameQueue players, the server offers this bandwidth to each one of each one of the players that declined its offers earlier. If one of the players takes the offer then this round. the offer of server. If b 1 , which is the bandwidth offered to player 1, is also the available bandwidth at the end of round 1, in round 2 the objective is to use this bandwidth to make a new offer