Game-Based Multi-MD With QoS Computation Offloading For Mobile Edge .
Game-Based Multi-MD with QoSComputation Offloading for Mobile EdgeComputing of Limited ComputationCapacityJunyan Hu1,2 , Chubo Liu1,2(B) , Kenli Li1,2 , and Keqin Li1,2,3(B)12College of Computer Science and Electronic Engineering, Hunan University,Changsha 410082, Hunan, al Supercomputing Center in Changsha, Changsha 410082, Hunan, China3Department of Computer Science, State University of New York,New Paltz, NY 12561, USAlik@newpaltz.eduAbstract. Mobile edge computing (MEC) is becoming a promisingparadigm of providing cloud computing capabilities to the edge network, which can serve mobile devices (MDs) with computation-intensiveand delay-sensitive tasks. Facing with high requirements of many MDs,it’s essential for MEC with limited computation capacity to serve moreMDs with QoS. For each mobile device, it is also desirable to have a lowenergy consumption with an expected deadline. To solve above problems,we propose a Game-based Computation Offloading (GCO) algorithm,which includes the task offloading profile and the transmission powercontrolling with the method of non-cooperative game. Our mechanismmaximizes the number of served MDs with deadline, as well as minimizing the energy consumption of each MD whose task is executed onMEC. Specifically, Given the allocation of transmission power, a GreedyPruning algorithm is proposed to determine the number of tasks executedon MEC. Besides, each MD adopts his/her transmission power controlling strategy to compete the computation resource of MEC or minimizethe energy consumption. A game model for illustrating the problem oftask offloading is formulated to find a proper transmission power for eachtask and is proved the existence of Nash equilibrium solution. Experiments are simulated to evaluate the proposed algorithm in terms ofeffectiveness evaluation.Keywords: Mobile edge computing · Nash equilibrium ·Non-cooperative game theory · Task offloading · Power controlling1IntroductionNowadays, Mobile Devices (MDs) are indispensable part in our daily life[1,2]. With the popularity of smart MDs, many new computation-intensive andc IFIP International Federation for Information Processing 2019 Published by Springer Nature Switzerland AG 2019X. Tang et al. (Eds.): NPC 2019, LNCS 11783, pp. 16–27, 2019.https://doi.org/10.1007/978-3-030-30709-7 2
Multi-MD and MEC Computiation Offloading System17delay-sensitive applications have higher demands on quality of service (QoS) [3].However, the limited resources of MDs e.g., battery, computation capacity, cannot meet their own needs. Therefore, how to meet the high QoS requirements ofmultiple MDs with low energy consumption is an urgent problem to be solved.Mobile edge computing (MEC) provides high-bandwidth, high-computingresources for nearby MDs to meet the high QoS demands for computationintensive and latency-sensitive applications via edge network [4,5]. For a multidevice MEC system with multiple parallel computation tasks requiring computing resources, MEC can be viewed as a small cloud with limited resources(processing speed, CPU cycle). Facing with resource requests from numerousdevices, MEC should propose a resource allocation strategy that maximizes thenumber of served MDs with QoS requirements. For each MD, it has an expectedvalue of delay, and on this basis, it is desirable to have a minimum energy consumption. The transmission rate and the received computation resource of eachMD are affected by other MDs. Thus, if there are many devices that offload theirtasks, the QoS experience of each MD will be deduced. In order to compete theresource for CPU cycle, a suitable transmission power controlling strategy mechanism for each MD should be proposed.The remainder of the paper is organized as follows. In Sect. 2, we introducethe related work. Section 3 describes the system model and presents the problemthat needs to be solved. In Sect. 4, we consider the problem as a non-cooperativegame and propose Algorithm GCO to compute the Nash equilibrium solution. InSect. 5, extensive experiments results indicate the feasibility of our algorithms.We conclude the works of this paper in Sect. 6.2Related WorkTask offloading for user requirements in MEC has been studied by many scholarsand most of studies are analyzed from computational offloading, latency, storage,and energy efficiency. [6–8] are considered from optimizing the energy consumption of users. In [6], Chen et al. computed the energy harvesting for MEC byusing Lyaponuv Optimization method. Besides, some works and models considered from guaranteeing the deadline or minimizing average delay [9–12]. Fanet al. proposed an application aware workload scheduling mechanism for IoTbased on MEC to minimize the average delay of application resource requestsin [10]. [11] solved the problem of minimizing delay by using the method of onedimensional search. And then in [13] and [14], Zhang and Chen et al. consideredthe proportional overhead on power consumption and latency. In addition, [15–17] optimized the transmission to achieve the offloading balance in the MEC bycontrolling the transmission power. In [15], Rodrigues et al. proposed a workloadbalance strategy for cloudlets to minimize the cost by using Transmission PowerControl (TPC). In [16], Mao et al. minimized the weighted sum of the executiondelay and energy consumption by optimizing the transmission. Different fromabove all, our work considers not only from the view of serving the maximumnumber of MDs with deadline constraint, but also from the perspective of eachMD’s minimum energy consumption.
18J. Hu et al.Game theory plays an increasingly important method in MEC [18–21]. In [18],Chen et al. analyzed the multi-task offloading problem for MEC under the condition of multi-channel from the view of game theory. In [21], by using the theoryof Minority Games, Ranadheera et al. proposed a novel distributed server activation mechanism for computation offloading which guaranteed energy-efficientactivation of servers as well as satisfaction of users quality-of-experience (QoE)requirements in terms of latency. Heuristically, our work introduces an adaptivetransmission power mechanism in the competing process for limited-computationresources provided by MEC. We formulate a non-cooperative game-based mechanism for MEC’s offloading decision making and MDs’ power control.3System ModelWe denote N {1, 2, . . . , N } as the set of N MDs, each of which hascomputation-intensive and time-sensitive task to be completed. Let τn be thetask of n, and the requirement of MD τn can be denoted as a tuple (cn , dn , Tn ),where cn denotes the total number of required CPU cycles, dn denotes the size ofthe input task data, and Tn denotes the expected time required to complete taskτn . The task can be computed either locally on the mobile device or remotelyexecuted on MEC via computation offloading. Therefore, we denote the decisionprofile X {x1 , x2 , . . . , xN } as the set of indicator function for N MDs, wherexn {0, 1}. If the task of MD n is computed on MEC S, xn 1, otherwise,xn 0. Besides, we denote J as the set of mobile devices, where J {n xn 1}.Here we consider the computational capacity of MEC S, denoted as C, is limited.If a MD prepares to offload his task to MEC S, the energy and time consumptionof communication and computation are considered.3.1Communication ModelIf MD n offloads task τn to remotely edge execution, the input data shouldbe transmitted to MEC servers of S. Given the decision profile X and J, thecommunication rate of MD n (n J) via the wireless channel can be denoted asrn (X, P) B log2 (1 pn Gn).η0 Σi J\{n} pi Gi(1)Here B is the channel bandwidth, and for simplicity, we only consider one channel. P {p1 , p2 , . . . , pN } is the transmission power profile of all MDs and eachpn can be chosen from the internal [pn , pn ]. Further, Gn , related to the environment and the distance, denotes the channel gain between MD n and MEC Sand η0 is the background noise power. In (1), let In Σi J\{n} pi Gi be the sumof interference from other MDs who belong to set J. Note that the transmissionrate can be affected not only the transmission power of itself but also the MDswhich offload tasks to MEC S.
Multi-MD and MEC Computiation Offloading System3.219Computation ModelIf task τn of mobile device n is offloaded to MEC S to execute, i.e., xn 1, thecompletion time will contain communication time and computation time. Wedefine the completion time astn,of f cndndncn ,pGnnrn (X, P) fnB log2 (1 η0 Σi J\{n} pi Gi ) fn(2)where fn is the computation capability (i.e., CPU cycles per second) assignedto MD n by the MEC S. Therefore, the energy consumption can be denoted asEn,of f (X, P) 3.3pn d nB log2 (1 pn Gnη0 Σi J\{n} pi Gi ).(3)MEC’s Resource Allocation StrategyFrom the perspective of MEC S with limited resource, serving as many MDs aspossible is its primary goal. We consider distributed resource allocation for MDs,and model it as max J with the constraints tn Tn , n J and n J fn C,Xwhere · is the number of elements in set ·.Theorem 1. The issue max J that maximize the number of tasks with QoSXexecuted on MEC is NP-hard.Algorithm 1. Greedy-Pruning algorithmRequire: N , P, G, B, C.Ensure: J, fn (J).1: J N , J1 { }, J2 { }; 2: Calculate each fn (J) (n J) based on Eq. (4); 3: while ( k J fk (J) C) do fj (J\{i})};4:J1 J1 {arg mini5:6:7:8:j J\{i}while (J1 J2 ) doJ2 J 1 ;for (l J2 ) do J1 (J1 \{l}){arg mini9:J N \J1 ;10: return J, fn (J). J \{l}j N1\{i} J \{l}fj ( N1\{l})};In order to solve the problem max J , we propose a Greedy-Pruning algo Xrithm (Algorithm 1). Let fn (J) be the critical point of computation capabilitythat MD n needs.
20J. Hu et al.fn (J) cnTn dnγn (X,P) fn (J).(4) Assuming n N fn C, then there is J N . Otherwise, MEC S needs tofilter out some MDs to maximize the number of beneficial MDs with QoS. InAlgorithm 1, J is the set of MDs to be selected, and J1 is the set of MDs to be fil tered out. In the outer while loop of the line 3–9, once k J fk (J) C, an appro Cpriate MD will be added to J1 to check whether the condition k J fk (J)is satisfied, where J is the updated J. In each round of preparation to remove as the objective function. But removinga MD to J1 , we use min j J fj (J) MD i in J that minimizes j J\{i} fk (J\{i}) directly does not guarantee thatupdated J is globally optimal. If there is always fj ((J {l})\{i}).(5)l arg minij (J {l})\{i}for any MD (l N \J), J is optimal.3.4Power Control Strategy of Mobile DeviceIn this section, we explore that how to minimize each MD’s energy consumptionwithin the expected delay range. As can be seen from Eq. (2), tn,of f decreases aspn increases. Given F and the expected time Tn required to complete the taskτn , tn,of f Tn can be introduced as followsdncnpn (2 (Tn fn )B 1)( η0 In) pn .Gn (6) We denote pn as the critical power of MD n. If pn pn , MD n will not choose to execute his task τn on MEC. We assume pn pn and consider the energy consumption of MD n in the internal [max{pn , pn }, pn ].In each round, MD n, who does not execute his task τn on the MEC, canincrease pn to provide his own competitiveness. This leads to two outcomes:removing one of the other MDs in J or adding to the set J directly.Removing one of the other MDs in J: Increasing pn to p1n and satisfying theconditions arg minfj (J3 \{k}) n, (J3 J {n}),kj J3mink fj (J3 \{k}) C.(7)j J3Adding to the set J directly: Increasing pn to p2n and satisfying the condition fj (J {n}) C.(8)j J {n}
Multi-MD and MEC Computiation Offloading System21Considering the energy consumption and pn pn , we define p n min{p1n , p2n , pn }, where p n is the updated pn in next round. We denote P ( p1 , p 2 , . . . , p N ). We propose a Binary search algorithm (Calculate P(·)) toupdate pn .44.1Game Formulation and AnalysesGame FormulationLet P n (p1 , · · · , pn 1 , pn 1 , · · · , pN ) be the transmission power profile of allMDs except MD n. Let Pn be the set of power and decision making strategies forMD n, i.e., pn Pn . Given other MDs’ transmission power P n , MD n wouldlike to select a proper decision pn to compete the computation resource of MECS and minimize his own energy consumption, under the condition of satisfyingQoS. The objective function of MD n can be written as follows min En (X, P).The strategy set of MEC S is X and his objective function is maximizing thebeneficial number of MDs J . Then, the multi-device computation offloadinggame can be represented as G, where G {(Pn )n N , X ; (En )n N , J }. Algorithm 2. Calculate P(·)Require: N , P, G, B, C, J, ε. Ensure: P.1: for n J do2:p n pn ;3: for n N \J do4:l1 pn pn , r1 pn pn ;5:l2 pn pn , r2 pn pn ;6:while ( r1 pn l1 pn ε ) do1 pn7:mid1 l1 pn r;28:if Conditions in Eq. (7) are satisfied then9:r1 pn mid1 ;10:else11:l1 pn mid1 ;12:p1n r1 pn ;13:while ( r2 pn l2 pn ε ) do2 pn14:mid2 l2 pn r;215:if Condition in Eq. (8) is satisfied then16:r2 pn mid2 ;17:else18:l2 pn mid2 ;19:p2n r2 pn ;20:p n min{p1n , p2n , pn }; 21: return P.For all MDs, P {p 1 , . . . , p N } is the optimal countermeasure strategy. That ) En (p n , P n). Foris to say, for MD n and any pn Pn , there is En (pn , P n MEC S and any X (x1 , x2 , . . . , xN ), J(X ) J(X) .
224.2J. Hu et al.Nash Equilibrium Existence AnalysisTheorem 1. Given N , G, B, C, and pn max{p n , pn }, non-cooperative gamestrategies for N MDs and MEC S M (N , {Pn }n N , {En,of f }; S, X , J ) havea Nash equilibrium P , X , (p Pn , X X ). E(X,P)n,of fProof. We easily know that 0 (pn 0). Based on Eq. (1) we can pnobtain that 2 rn (X, P)BG2n .(9) p2nln 2(η0 In pn Gn )2En,of f (X, P) is taken the second derivative with respect to pn , and it yields that 2 En,of f11dn B 2 Gn2[( 1 ) log2 μ (1 )], 23 pn(η0 In )μrn ln 2μln 2μ pn Gnwhere μ η0 Iη0n Iand μ 1.nLet function g(x) ( 1 x1 ) log2 x and its derivative for x is g (x) 2ln 2 (1(10) x1 ). We analyse function g(x), x ln 2 log2 x 1.x2 ln 2(11)Let function s(x) x ln 2 log2 x. When x 1, s(x) is monotonically decreasing, and s(x) s(1) 0. Therefore, when x 1, g (x) 0, g(x)is monotonically decreasing, and g(x) g(1) 0. Because μ 1, the second derivative of En,of f (X, P) with respect to pn is always less than 0, i.e., 2 En,of f p2nn,of f 0 (pn max{p n , pn }). Based on 0 and the power pnvariable of each MD is a closed interval, En,of f (X, P) takes the minimal value when pn max{pn , pn }. Thus, p n max{p n , pn }, and for any pn p n , there ) En (p n , P n).always is En (pn , P n first set in Algorithm Greedy-pruning that satisfies theFor MEC S, J is the following conditions: (1) k J fk (J ) C; (2) for any MD l N \J , there isalways l arg minfj ((J {l})\{i}). Ei(X,P)j (J {l})\{i}Then, the maximum number of beneficial MDs with QoS will no longer decrease.Therefore, for any offloadingscheduling profile X X satisfying the conditions xn tn Tn , n J and n J fn C, there always will be J(X) n N xn . J(X ) n N4.3Nash Equilibrium Solution ComputationWe propose a Game-based Computation Offloading (GCO) Algorithm 3 to findthe equilibrium solution.
Multi-MD and MEC Computiation Offloading System23Algorithm 3. Game-based Computation Offloading (GCO)Require: N , P, P, G, B, C, ε, δ.Ensure: P, J, X.1: N (0) N ;2: s 1;3: pn (0) P(N (s 1));4: J(0), fn (J(0)) GP(N (0), pn (0), G, B, C);5: t 0;6: while P (t 1) P (t) δ do (t), pn (t), G, B, C, J(t), ε);7:pn (t 1) Calculate P(N8: J(t 1), fn (J(t 1)) GP(N (s), pn (t 1), G, B, C);9:t t 1;10: J J(t);11: N (s) N (s 1);12: while (N (s) N (s 1)) do13:s s 1;14:loop steps 3 to 11;15: return P, J, X.55.1SimulationsSimulation SettingsWe evaluate the system performance of the proposed GCO based on the interaction of MEC S and multiple mobile devices in this section. We consider 50MDs in this system. The size of the input task data dn of each MD n is randomly selected from the interval (0, 2] MB and the total number of requiredCPU cycles cn dn · wn , where wn is the workload requirements of task τn(wn [100, 500] cycles/bit). Similarly, the expected Time Tn of MD n alsofollows a uniform distribution with (0, 3]s. The minimum transmission powerpn is 100 mW, and the maximum value is randomly selected from the interval[1000, 3000] mW. We consider MEC S has a coverage range of 50 m. The computational capacity C of MEC S is 1GHz. The bandwidth B 10 MHz andthe background noise power η0 100 dBm. Based on the wireless interferencemodel for urban cellular radio environment, the channel gain Gn disαn , wheredisn is the distance between MD n and the MEC S and α 4 is the path lossfactor.5.2Convergence of Algorithm GCOFigures 1 and 2 illustrate the convergence process of transmission power for eachMD by executing our proposed GCO algorithm. With the number of iterationsincreasing, the transmission power of each MD is increasing and then the curvereaches to a stable value. During the process of computing, some MDs willwithdraw the resource competition if the transmission power is higher than theiraccepted maximum value, i.e., pi pi . Figure 2 is the transmission power curveof MDs who cancel to compete the computation resource of MEC S. Moreover,we can know that the transmission power can be obtained after 6 iterations,which shows high efficiency of our proposed algorithm.
24J. Hu et al.Fig. 1. Change of transmission power and beneficial MDs in the iterative process.Figures 3 and 4 is a curve of the number of MDs who obtain computingresources provided by MEC S and a bar graph of the average energy consumptionduring the iterative process, respectively. At the beginning, each MD’s transmission power is set as the initial value, i.e., the minimum value. The number ofMDs with QoS served by the MEC S with limited computing resources is 23 andthe average energy consumption is about 70. Each MD increases its transmissionpower to complete for the computing resources of MEC S, which causes the average energy consumption to rise during the iteration, as shown in Fig. 4. In Fig. 3,after several rounds of mutual negotiation between MDs, the number of MDswho can use the computing resources provided by MEC S gradually increasesand maintains stable at the value 29 as the number of iterations increases.Fig. 2. Change of transmission power and non-beneficial MDs in the iterative process.
Multi-MD and MEC Computiation Offloading System25Fig. 3. The process change of number of beneficial MDs.Fig. 4. The process change of average energy consumption.5.3Performance EvaluationThe performance of GCO algorithm is evaluated from two respects: the numberof iterations and the execution time. The variable is the number of MDs N ,which increases by 10 from 10 to 50. For each N , we repeat the experimentmany times. The experimental results are shown in Figs. 5 and 6.Figures 5 and 6 show the number curve of iterations and iterative time curveof Algorithm GCO as the number of MDs increases, respectively. The blue lineis an average curve in each figure. In Fig. 5, the general trend of the curveincreases linearly and slowly. Besides, even if the number of MDs is 50, theaverage number of iterations is very small. In Fig. 6, as the scale of MDs increases,the computation overhead curve increases in a polynomial. The red dashed lineis the trend line of the computation overhead curve, which is a second orderpolynomial. The fitting degree of the trend line and the time curve is 0.9908.When the number of MDs reaches 50, the average overhead is 225 ms, which israpid and shows the high efficiency of our proposed algorithm.
26J. Hu et al.Fig. 5. Average iterative times of different scales of MDs. (Color figure online)Fig. 6. Computation Overhead of different scales of MDs. (Color figure online)6ConclusionsOur study focuses on the task offloading problem of one MEC and multiple MDswith delay deadlines. From the perspective of non-cooperative game theoreticalmethod, the number of served MDs with delay deadline and the energy consumption of all tasks executed on MEC S are alternately optimized. We prove theexistence of Nash equilibrium solution and propose GCO algorithm to solve it.Besides, the convergence of the algorithm is also analyzed. Extensive simulatedexperiments results validate and show the feasibility of our proposed method.Acknowledgments. The research was partially funded by the National Key R&DProgram of China (Grant No. 2018YFB1003401), the Program of National NaturalScience Foundation of China (Grant No. 61751204).References1. Abbas, N., Zhang, Y., Taherkordi, A., Skeie, T.: Mobile edge computing: a survey.IEEE Internet Things J. 5(1), 450–465 (2018)
Multi-MD and MEC Computiation Offloading System272. Porambage, P., Okwuibe, J., Liyanage, M., Taleb, T., Ylianttila, M.: Survey onmulti-access edge computing for internet of things realization. IEEE Commun.Surv. Tutor. 20, 2961–2991 (2018)3. Ning, Z., Wang, X., Huang, J.: Mobile edge computing-enabled 5G vehicular networks: toward the integration of communication and computing. IEEE Veh. Technol. Mag. 14, 54–61 (2018)4. Kai, W., Hao, Y., Wei, Q., Min, G.: Enabling collaborative edge computing forsoftware defined vehicular networks. IEEE Netw. 32, 112–117 (2018)5. Guo, H., Liu, J.: Collaborative computation offloading for multiaccess edge computing over fibercwireless networks. IEEE Trans. Veh. Technol. 67(5), 4514–4526(2018)6. Chen, W., Dong, W., Li, K.: Multi-user multi-task computation offloading in greenmobile edge cloud computing. IEEE Trans. Serv. Comput. 99, 1 (2018)7. Yang, L., Zhang, H., Ming, L., Guo, J., Hong, J.: Mobile edge computing empowered energy efficient task offloading in 5G. IEEE Trans. Veh. Technol. 67, 6398–6409 (2018)8. Feng, W., et al.: Joint offloading and computing optimization in wireless poweredmobile-edge computing systems. IEEE Trans. Wirel. Commun. 17(3), 1784–1797(2017)9. Min, C., Hao, Y.: Task offloading for mobile edge computing in software definedultra-dense network. IEEE J. Sel. Areas Commun. 36(3), 587–597 (2018)10. Qiang, F., Ansari, N.: Application aware workload allocation for edge computingbased IoT. IEEE Internet Things J. 5(3), 2146–2153 (2018)11. Liu, J., Mao, Y., Zhang, J., Letaief, K.B.: Delay-optimal computation task scheduling for mobile-edge computing systems. In: IEEE International Symposium onInformation Theory, April 201612. Xiang, S., Ansari, N.: Latency aware workload offloading in the cloudlet network.IEEE Commun. Lett. 21(7), 1481–1484 (2017)13. Jiao, Z., et al.: Energy-latency trade-off for energy-aware offloading in mobile edgecomputing networks. IEEE Internet Things J. 5, 2633–2645 (2018)14. Chen, X., Jiao, L., Li, W., Fu, X.: Efficient multi-user computation offloading formobile-edge cloud computing. IEEE/ACM Trans. Netw. 24, 2795–2808 (2016)15. Rodrigues, T.G., Suto, K., Nishiyama, H., Kato, N., Temma, K.: Cloudlets activation scheme for scalable mobile edge computing with transmission power controland virtual machine migration. IEEE Trans. Comput. 67, 1287–1300 (2018)16. Mao, Y., Zhang, J., Letaief, K.B.: Joint task offloading scheduling and transmitpower allocation for mobile-edge computing systems. In: Wireless Communicationsand Networking Conference (2017)17. Tao, X., Ota, K., Dong, M., Qi, H., Li, K.: Performance guaranteed computationoffloading for mobile-edge cloud computing. IEEE Wirel. Commun. Lett. 6(6),774–777 (2017)18. Xu, C., Lei, J., Li, W., Fu, X.: Efficient multi-user computation offloading formobile-edge cloud computing. IEEE/ACM Trans. Netw. 24(5), 2795–2808 (2016)19. Hu, X., Wong, K.K., Yang, K.: Wireless powered cooperation-assisted mobile edgecomputing. IEEE Trans. Wirel. Commun. 17(4), 2375–2388 (2018)20. Li, K.: A game theoretic approach to computation offloading strategy optimizationfor non-cooperative users in mobile edge computing. IEEE Trans. Sustain. Comput.99, 1 (2018)21. Ranadheera, S., Maghsudi, S., Hossain, E.: Computation offloading and activationof mobile edge computing servers: a minority game. IEEE Wirel. Commun. Lett.7, 688–691 (2018)
For a multi-device MEC system with multiple parallel computation tasks requiring com-puting resources, MEC can be viewed as a small cloud with limited resources (processing speed, CPU cycle). Facing with resource requests from numerous devices, MEC should propose a resource allocation strategy that maximizes the
Game board printable Game pieces printable Game cards printable Dice Scissors Directions Game Set Up 1. Print and cut out the game board, game pieces, and game cards. 2. Fold the game pieces along the middle line to make them stand up. 3. Place game pieces on the START square. Game Rules 1. Each player take
[12] have developed a computer-based game called 'Golden Sugarcane', designed for young Thai students. The game is a competition-based game, allowing students to learn mathematics while they are playing on the game without feeling bored. An online game named 'Eternal Story' is also a well-known game based learning technique, which has
Design Your Own Game In this assignment, you will be designing your own game on your own in groups of 2. The game should be the type of game that you would play at a carnival, amusement park or casino. It cannot be a game that already exists— your group must create a unique game. Your game
During the Russian Game Developer's Conference, KRI-2004. . Your primary game input device is a computer mouse. You can control Dude, the main character, by clicking . - "Resume game": resumes current game, leaving the Game Menu. - "New game": starts a new game. W
game boy gallery 2 game boy wars game boy wars turbo game boy wars turbo - famitsu version game de hakken!! tamagotchi game de hakken!! tamagotchi - osutchi to mesutchi game de hakken!! tamagotchi 2 gamera - daikaijuu kuuchuu kessen ganbare goemon - kurofunetou no nazo ganbare goemon - sarawareta ebisumaru ganso!! yancha maru gb basketball gb .
The Battleship game was released as a plastic board game by the Milton Bradley Company (1967) The game has been popularized under the name "The Battleship game" by the Milton Bradley Company as it was published as a plastic board game in 1967. 4.1 The Original Battleship Game We provide description of the Battleship game as an interactive
Game Maker V7000 Chop Top* VMPL0Cxxx G678 G595 Game Maker V7000 Casino* VMPL0Wxxx G676 G595 Game Maker V7000 Slant Round Top VMPL0Dxxx G679 Game Maker V7000 14" VMPL0Nxxx G588 G591 Game Maker V7000 20" VMPL0Qxxx G612 G583 Game Maker V7000 Bartop VMPL0Fxxx Game Maker V7000 Slant (France) VMPL0Sxxx G605/G679 G708# Game Maker .
Football Junior Year 1965 Spoiler Alert: Scores for this year Game 1: Farrell 36 St. John’s Prep 0 Game 2: Farrell 20 Curtis 12 Game 3: Farrell 20 Poly Prep 0 Game 4: Farrell 40 Fordham Prep 0 Game 5: Farrell 0 New Dorp 0 Game 6: Farrell 34 Brooklyn Prep 6 Game 7: Farrell 42 Xavier 0 Game 8: Farrell 35 Brooklyn Tech 21 .
