Graphics and game theory

This step is not compulsory. The size is being reduced to just simplify the problem. The game can be solved without reducing the size also. After reducing the above game with the help of dominance property we get the following game. Step 2: Let x be the probability of selection of alternative 1 by player A and 1 — x be the probability of selection of alternative 2 by player A.

Derive the expected gain function of player A with respect to each of the alternatives of player B. Similarly, the second alternative of player B is column number 2, so multiply 2 with x and -9 with 1 — x and add them.

Similarly, the third alternative of player B is the column number 4, so multiply -6 with x and 4 with 1 — x and add them. Please refer the shown table. See the table below:. Skip to content. Change Language. Related Articles. Table of Contents. Improve Article. Save Article. Then these extensions are classified based on information exchanged.

Finally, characterization of all possible values gained from this abstract extension is described. Okamura et al. They investigated the learning of the behavior of variable-structure stochastic automata in a game.

These automata have learning capabilities and can update their actions. The players have a lack of information of payoff matrix. After every play, the environment, responds to automaton actions. After this, players update their strategies. Sauder and Geraniotis have worked on maximin and minimax theorems. They formulated signal detection process as two-players zero-sum game.

The two-players are the detector designer and the signal designer. The signal detection problem arises when analyzing the signal is genuine or deceptive. Finally, results are validated via simulation. Hellman have focused on rational belief system.

The study got the basis from the work of Aumann and Dreze. They described that players have common knowledge of rationality. Whereas in this article, it is argued that there is no need of common rationality. Finally, it is shown that the expected payoff in the game is only the minimax value. Ponssard have discussed minimax strategies. These are prohibited to give particular solutions in optimal zero-sum game play. This study finds a strategy to be used after the mistake carries out in play.

There are two approaches proposed to get optimal strategies. The first approach arrived from perturbed games. The second approach established on the basis of the lexicographic application.

If the opponent ignores mistakes, the strategy will remain optimal as it does not turn to give a loss. Gawlitza et al. One is max-strategy and the other is min-strategy for static program analysis.

These algorithms perform within a common general framework to solve v-cam cave equations. Rock paper scissors RPS is a cyclic game with three strategies. The game is 2-players zero-sum. The game rules are rock wins over scissors, scissors over paper and paper over rock.

Following papers considers RPS game theoretic model. Rock paper scissors is a three strategic 2-player game. According to game rules rock beats scissors, scissors beat paper and paper beats rock.

The game will draw if both players show same options. Sinervo and Lively have used cyclic RPS game in a biological study. By using this zero-sum model they studied three different strategies of male side-blotch lizards. It studies territory use and patterns of sexual selection on male side-blotch lizards.

They characterized Nash equilibria into two sets. With an even number of actions, an infinity of Nash equilibria exists. On the second set with an odd number of actions unique Nash equilibria is found.

This paper studies the strength of Nash equilibria. Frey et al. This is realized by analyzing agents independently playing a multiplayer mod game.

The game is like the rock paper scissors. The behavior of players in human groups is non-fluctuating and effective. In this game the periodic behavior is stable.

Batt has also studied the model of Rock Paper Scissors game and has presented insights of the game having an efficient outcome with few conflicts. The game players are biased for being a winner. This game is not efficient with major conflicts.

For that other approaches like coin-flip is the best choice. Neumann and Schuster have used a zero-sum rock scissor paper game as a framework. By which they modeled the process of bacteriocin producing bacteria.

The game is examined for three strains. These are of E. They derived stability criteria for these strains. Duersch et al. There is no pure equilibrium exists in RPS game. They found that pure equilibrium strategy exists only in non-generalized rock paper scissors game.

It also showed that pure equilibrium exists for the 2-player finite symmetric game. Cake cutting is a simple child game. In this game, the first player has to cut the cake and then the second player has to choose the piece.

The first player has to cut pieces equally. Otherwise, the second player has the choice to choose either the bigger piece or the smaller one. This is to accomplish honesty in the game. Cake cutting is a simple game in which first player has to cut the cake and second player will then choose any piece.

This is game of fairness as if player cuts unequal pieces then other player has the option to choose either the bigger or smaller piece. Otherwise both players will get equal pieces. Procaccia have discussed cake cutting game. They described that it is a powerful tool to divide heterogeneous goods and resources.

Cake cutting algorithm looks for formal fairness in the division of heterogeneous divisible goods. But the design of these algorithms is a complex task for computer scientists. Edmonds and Pruhs have proposed a randomized algorithm that considers cake cutting algorithm. It equally allocates resources between n numbers of players. This algorithm needs honesty of players. Matching penny is also a zero-sum 2-player game.

Both players secretly turn their coins and then compare with each other. If both are heads or tails then the first player will win else player 2 will win both coins. Matching pennies is a simple zero-sum 2-player game. Both players turn their coins secretly and then show.

If both coins are of same side c , d first player will win else second player will win both coins a , b. McCabe et al. The Naive Bayesian learning and sophisticated Bayesian learning are studied in this context. These approaches examine that estimated mixed strategies can be played or not. Results showed that players do not use sophisticated Bayesian learning to obtain Nash equilibrium. Stein et al. This study constructs examples to support polynomial games.

Here Nash equilibria are representable as finitely moments. Whereas polynomial games cannot be represented as finitely moments. Colonel Blotto is a universal game providing a way for resource allocation. The two colonels simultaneously distribute resources over battlefields. The player devoting the most resources wins that battlefield. The payoff is equal to the total number of battlefields won. Colonel Blotto is a resource allocation game. In this game the two colonels simultaneously distribute limited resources over several objects or battlefields.

The player devoting the most resources wins that battlefield, and the payoff is equal to the total number of battlefields won. Roberson described the remarkable equilibrium payoffs in the Colonel Blotto game. It considers both symmetric and asymmetric cases of the zero-sum game. The proportion of won battlefields is the payoff of player. Hart have studied Discrete Colonel Blotto game. This is a Zero-sum game with the symmetric case for which optimal strategy is obtained.

Both of these games deal with the conflicting environment. Kuhn Poker is a simplified form of Poker developed by Harold W. Kuhn Tucker In this 2-player game, the deck includes only three cards. One card is distributed to each player. The first player has to bet or pass then the second player may bet or pass. On a bet, the next player must bet also. When both players pass or bet then the player with the highest card will win the pot. Southey et al. There main concern is opponent modeling in the game.

They studied two algorithms, expert and parameter estimation. Their experiment showed that learning methods do not give good results in the small game.

This is a Zero-sum game between two players, Princess and Monster. The game played on 2-D search set. When the distance between both players is less than r then Princess got captured and Monster wins.

Wilson has developed this game on a circle. Princess and Monster move on a circle either clockwise or anti-clockwise. If both players move in the same direction, the game state does not change. But if they move in opposite directions then there will be a point on the circle on which both reach at the same time. At that point, Princess got captured and Monster wins. We have discussed before that game describes strategic interactions.

In game theory, the solution concept is like a rule by which game theorists seeks how the game will be played. The Nash equilibrium, Pareto optimality, and Shapley values are different known solution concepts. These concepts are used to formally predict that how the game will be played.

Nash defined Nash equilibrium. And no utility a player can have by changing its own strategy only. For example, there is a game battle of sexes Shah et al. The game is between husband and wife. Husband prefers to go for football match and wife wants to go for a concert. Also, they want to go together. The payoff table is shown in Table 2. The solution for the game can be either both go for a football match or go to a concert.

Singh and Hemachandra have studied Nash equilibrium for stochastic games with independent state processes. This study got basis from the work of Altman et al.

They worked on N-player Constrained Stochastic games. Grauberger and Kimms have computed Nash equilibria for network revenue management games. This study investigates network management competition. A heuristic is presented for computing Optimal Capacity allocations. It also computes Nash equilibria in non-zero-sum games. It computes approximate to exact Nash equilibrium. They used the linear continuous model to reduced computational time. Gharesifard and Cortes have considered a network based scenario and obtained a Nash solution.

The two players are two network agents. Both agents with opposite aims make a zero-sum game between them. The saddle-point dynamics for concave-convex class converges to Nash equilibrium.

This saddle-point dynamics do not work to converge directed networks. Porter et al. One method is for the two-player game and the second method is for the n-player game. Both methods uses backtracking approaches to search the space of small and balanced support. These methods are tested on different games. Results showed positive performance of these methods. Another approach the Lemke—Houson algorithm for two-player games also discussed here.

Rosenthal have obtained correlated equilibria for 2-player games. These are more general strategies than Nash equilibrium known as correlated equilibrium.

There can be a player who prefers correlated equilibria on Nash equilibrium. If this so, then correlated equilibria is a convenient solution. If the game is the best response then the correlated equilibria are not the right solution.

It is good for the competitive games. Hu and Wellman have computed Nash equilibrium for the general-sum stochastic game. They proposed a method for a multiagent Q-learning. The method Nash-Q generalizes Q-learning of single-agent to the multiagent environment. It updates its Q-function by assuming Nash equilibrium actions as a choice of agents. It is shown that Nash Q provides efficiency to get equilibrium on single-agent Q-learning.

This is an offline learning process. The online version of this learning process is also implemented. Maeda have considered games that have fuzzy payoffs. They first characterize equilibrium strategies as Nash equilibrium strategies. Then they examine characteristics of game values of fuzzy matrix games.

Finally, they demonstrated this approach via numerical example. Athey have studied games known as games of incomplete information. They proposed a restriction called single crossing condition SCC for these games. In these games, players have private information of their own. The results of this study show non-decreasing Pure Strategy Nash equilibrium. The proposed approach is constructive. So that the equilibria can be calculated for finite action games easily.

Pareto optimality introduced by Vilfredo Pareto Yeung For example, when Economy is competitive perfectly then it is Pareto optimal. This is because no changes in the Economy can make better the gain of one person and can make worse the gain of another person at the same time. Feldman has discussed Pareto Optimality in bilateral barter. The proved the constraints under which trade moves go on to pairwise optimal allocation. Then this paper discussed some general conditions by which these allocations are Pareto optimal.

Kacem et al. Their proposed approach combines Fuzzy logic and evolutionary algorithms. This combination minimizes machine workloads and completion time. Guesnerie have discussed insights of non-convex economics. The paper characterizes Pareto-optimal states.

Then analyze how to achieve them in distributed economy. The focus of this paper mainly concerns with conditions needed for optimality, marginal cost pricing rules, and decentralized non-convex economy. There is a Shapley value another solution concept used in cooperative game theory Shapely It allocates a distribution to all players in a game.

The distribution is unique and the game value depends on some desirable abstract characteristics. In simple words, Shapley value assigns credit among a group of cooperating players.

For example, there are three red, blue and green players. The red player cooperates more than blue and green players. The goal is to form a pair and then assign credits to them.

Each pair must have a red player as it cooperates more than others. So there can be two possible pairs. The two pairs are:. The red player cooperates more, so it will get more profit than player blue in the first pair. Similarly, it will get more profit than a green player in the second pair. Littlechild and Owen discussed the problem of computing Shapley value for large games. They considered the work of Broker and Thompson of about aircraft landing charges on the airport.

This paper presents an expression that can be calculated when the cost function is a characteristics function. The costs of the biggest player in any subset of players is equal to the cost of that subset. Gul has worked on the bargaining problem in a transferable utility economy.

A framework is established by which the two approaches, cooperative and noncooperative, are compared. The stationary subgame perfect Nash equilibrium is used and with small time intervals, the gain is the Shapley value for the agent. It is a two-phased play. The first phase is of bidding that gives the winner of the game. In the second phase the winner is rejected then the game is again played without that winner.

This paper describes that the payoff of the game coexists with Shapley value. Parsons and Wooldridge have discussed both game and decision theories.

Decision theory seeks to get the most favorable choice. That can maximize utilities of decision makers. Whereas the game theory also studies self-interested agents. It takes agents as greedy players want to maximize their own gain.

This paper reviewed existing literature. Then it revealed issues related to autonomous agents and multi-agent system. Hart et al. They obtained game value and derived utility simultaneously by using decision theory. They found the gap between the axioms and presumption about expected utility maximization.

Axioms characterize expected utility maximization, considering risk, in the individual decision. The presumption is that expected utility maximizers evaluate the game by their value. This study does not fill this gap completely. Because rationality involves playing maximin strategies is not proved.

This paper explores current research formats in AGT. The research theme is different here than classical game theory. AGT receives the computational difficulty as a coupling requirement which makes it unique. Wooldridge have explored the feasibility of game theory applications in computer science.

They discussed issues related to the application of game theoretic models. They revealed the incorrect use of game theory model. They also mentioned that more research is needed in this area. Ahmad and Luo have proposed an algorithm for video coding. It considers optimization of rate control. In this two-level algorithm, the first level is about the target bits allocation.

In the second level, each MB computes to share bits fairly. So that its quantization scale can be optimized. In this section, we will discuss game theory applications in social groups and others. In social groups, people interact and communicate each other. To model behaviors in such communication, game theory has been used. Chen and Liu have modeled human behavior in social networks by using game theory.

This is the study of the impact of social networks in our daily life. This generalized approach can be used for several social networks. The efficiency and fairness between users are main considerations of the model design. Hand has discussed social conflicts and social dominance. The social dominance based on Leverage is considered here. There are personals having greater resources and personals having fewer resources as well.

The paper describes that game theory can be used to make less dominant individuals equal or greater to others. Altman have used Markov games to control the flow of arriving packets. These are the collection of normal-form games that agents play repeatedly. These games together with a value iteration algorithm are used for single controller. The controller design policies to control the flow.

Markov games is another name of stochastic games. This study reveals the existence of the stationary optimal policy. Ghosh and Goswami have studied semi-Markov game. They first transformed the model into the completely observed semi-Markov game.

Then they worked and obtained saddle-point. They showed the existence of saddle-point but with some conditions. Laraki et al. It describes conditions for the existence of game value. With these conditions the player 2 gets an optimal strategy for subgame perfect. The conditions described that payoff is a bounded function f. The function f is measurable and is lower semi-continuous. The model is based on some assumptions. That is the current price of product and market positions influenced future market positions.

This provides a way to get balance benefits gained from price variations. Sirbu has studied zero-sum games. The paper discussed stochastic differential game restricted to elementary strategies. The result shows the existence of value in a game with these strategies.

Pham and Zhang have studied 2-player zero-sum weak formulation game. The game discussed is Stochastic and Differential game. The game value is obtained by visocsity solution. The paper showed the value of the game as a random process. Hernandez-Hernandez et al. The game is between controller called minimizer and stopper called maximizer. The controller selects a finite-variation process. And the stopper selects time at which the game will stop.

The study described that the obtained optimal strategies are not unique. Oliu-Barton has worked on Finite Stochastic game. This is a zero-sum game. The paper proves the presence of value in the game. The aim of the study is to provide asymptotic behavior of strategies. These equations have terms. Their resulted solution is also a stochastic or random process. The paper presents a remarkable solution and showed the value in the game. Shmaya have studied an interesting game with one informed player.

It is a two-player zero-sum game with stochastic signals. The properties of this function, examined, shows that every player has a positive value of information in zero-sum game. In non-zero-sum games, there exists a universally agreed solution.

It means there is no single optimal solution as zero-sum games have. These games model cooperation instead of conflicts. There can be a win-win solution of game where everyone is a winner. The players can play a game while cooperating each other to achieve a common goal. Sullivan and Purushotham have discussed a high-level summit on non-communicable disease NCD. The summit held in New York on September in which they discussed cancer policies. The summit recognized cancer a first high-level disease.

This paper critically examined these policies. It gives an alternative solution based on a non-zero-sum game model for international cancer policy. Bensoussan et al. They modeled performance of two insurance companies. Each company is greedy to maximize its own utility.

The surplus process modeled by a continuous-time Markov chain and an independent market-index process. The game solved by a dynamic programming principle. It is also mentioned that the presented game can be extended to several directions.

Carlson and Wilson have considered failure in the management of U. But in this paper, a non-zero-sum game theoretical model is developed. It examines the effects of these changes on outcomes. It is analyzed that some changes do not affect outcomes and some have potential impact.

Shenoy and Yu have studied partial conflict games. This study examines the reciprocative strategy to induce cooperation.

Reciprocative behavior is defined as Non-Zero-sum games. It describes conditions for cooperative behavior to give an optimal response to reciprocative behavior. The feasibility of playing reciprocative strategy is also determined. Finally, conditions are given for reciprocative strategy that results to Nash equilibrium.

Mussa have studied two monetary units, euro, and dollar. This article argues that there is a non-zero-sum game between both units. It defines euro beneficial for both the euro area itself and rest of the world.

It is described that euro and the dollar are co-equal monetary standards. And is beneficial to the United States, euro area itself and rest of the world.

Semsar-Kazerooni and Khorasani have studied multi-agent system that considers cooperative game theory. The common goal of the multi-agent team is to have consensus. This paper is a series of work. In this paper, a previously introduced strategy is used called semi-decentralized optimal control strategy. Khosravifar et al. There is a distributed environment in which agent cooperates each other.

The performance of agents is analyzed by using non-zero-sum model. The decision-making process is also analyzed. Radzik have obtained pure-strategy and Nash equilibrium for 2-player non-zero-sum games. The payoff functions are upper semicontinuous. Agents are not allowed to interact each other in the model considers here. The optimality criterion dominant is the NE vector. This vector computes optimal actions of all players considering their payoff function.

The paper emphasizes solutions in pure strategies. Radzik have computed Nash equilibria for discontinuous two-person non-zero-sum games. This study examines two classes of these games on the unit square. Here the payoff function of the first player is convex or concave in the first variable.

This supposition combined with bounded payoff function entail the presence of Nash equilibria. The networks provide an excellent way of communication as well as support for distributed environments. The Game theory models have their obvious applications in network-based systems. The following papers use game theory to get optimal strategies for network problems.

Bell et al. By this approach, hyperpaths are generated between population centers and depot locations. They used a case study in the province of China to facilitate the proposal. Optimal hyperpaths are defined by using mixed strategy Nash equilibrium. Which give ultimate depot locations.

These depot locations are found by using two forms of drop heuristic. These heuristics gives optimal solution except in one case. That is when the most appropriate location for only one rescue center is obtained. Alpcan and Buchegger have studied vehicular networks. They examine security of network for the improvement of transportation. It is to provide optimal strategies to defend malicious threats. Three types of security games are studied here.

When players knows the payoff matrices the game is a zero-sum. When they know approximate payoffs the game is a fuzzy game. Perea and Puerto have used game theory approach in network security. The game is between the network operator and attacker. The operator establishes network to achieve some goals. While the attacker wants to place damages in the network. The optimal strategy for the operator is building a network.

The optimal strategy for attacker is finding edges to be attacked. This paper revealed dynamic aspects of the game. Bell has proposed a novel method to identify failure nodes. It is a two-player game between a router and virtual network tester. Router has to find a least-cost path, whereas network tester wants to increase trip-cost. The link in use are optimal for router and failure links are optimal for network tester.

Network tester fails link to increase trip-cost. So the given maximin method is to identify those links that threaten to network. Kashyap et al. The players, maximizer and minimizer, have mutual information. On both maximizer and minimizer there is total power constraint. They obtained saddle-point of the game. It is shown that minimizer has no need of channel input knowledge. Wei et al. In this problem jammer has a lack of information about actually transmitted signals.

There is a Zero-sum game between transceiver pair and jammer in the parallel fading channel. This paper explored CSI and solved problems related to it. The study finds equilibrium based on pure strategy. The game model adopts frequency hopping to defend against jam threats. Chen et al. The approach examines communication across cooperative and malicious relays.

It also analyzes the impact of this communication. The malicious relays can jam the network and they intentionally interrupt the system. The Nash equilibrium is determined to get optimal signaling strategies for cooperative relays.

Venkitasubramaniam and Tong have studied network communication. They used zero-sum game theoretic approach to provide anonymity. Optimizing anonymity problem is a game between network designer and adversary.

The model showed the presence of saddle-point. The approach obtained optimal strategies by using parallel Relay networks. It explores throughput tradeoffs in large networks. Wang and Georgios have considered Jammer and Relay problem. They modeled the problem between them as zero-sum mutual information game. By assuming source and destination being unaware optimal strategies are derived for both players.

In fading scenario, J cannot distinguish between Jamming and source signal. So the best strategy is to jam with Gaussian noise only. Here R forward with full power when jam link is worst. They derived optimal parameters on the basis of exact Nash equilibrium. Zhao et al. They used game theoretic approach for increasing performance of MAC protocols. This is an iterative game having two steps. In the first step current state of the game is determined on each node.

In a second step, the equilibrium strategy of the node is adjusted to the determined state of the game. The process is repeated till the desired performance is achieved. Larsson et al. They demonstrated basic concepts of conflicting and cooperative game theory through three examples of interference channel model.

For conflicting case the study is limited to Nash equilibrium and price of anarchy PoA. The Price of anarchy gives cost measures that system paid to operate without cooperation. Nguyen et al. They proposed an agent-based conceptual strategy. Which resolves the conflicting interests between product agents and network agents. The method is based on cooperative game theory that integrates and solves conflicting interests.

Finally, the approach is verified by simulation with two case studies. First is like micro grid example and the second is the more complex case. Quer et al. The scenario is about two ad hoc wireless networks.

Both cooperates together to gain some benefits. Statistical correlation between local parameters and performance is computed by Bayesian networks method. Both networks share their nodes to achieve cooperation. Game theory is used in nodes selection process.

The system level simulator is used to confirm results. Results showed that increase in performance can be achieved by accurate selection of nodes. Spyridopoulos have modeled problem of cyber-attacks. For that, they used Zero-sum one-shot game theoretic model. Single-shot games are opposed to repeated games. These models can be used when cooperation cannot be possible among players. The study explored adjustments and ideal techniques for both assailant and keeper. The study revealed a solitary ideal method for the keeper.

The ns2 network simulator is used for the simulation of the model. Khouzani et al. Malware has to maximize the damage. And the network has to take robust defensive strategies against attacks. This makes the game a Zero-sum game. Simple robust defensive strategies are shown via dynamic game formulation.

Finally, performance is evaluated through simulation. Ye et al. They analyzed model theoretically and verified via simulation. One can realize rationality and adaptability from a macro level. They showed that agitating effect of rewiring is effective than the zero-sum game. The algorithm provides a solution for Riccati equation. They discussed two schemes of programming. One is heuristic dynamic and second is dual. These schemes used for the solution of the value function and game costate.

Liu et al. It is based on the class of discrete-time constrained systems. This iterative adaptive dynamic programming algorithm provides a solution for near-optimal control problem. The control scheme has three neural networks. These networks are taken as parametric structures to assist the proposed algorithm. This is described by two examples that showed the practicality and concurrence of the algorithm. An algorithm is proposed for solving algebra rectaii equation.

They developed two versions, offline and online. An offline version is a model-based approach. The online version is a model-free approach but partially. These approaches are validated through simulation.

Abu-Khalaf et al. They provide practical solution method for suboptimal control of constrained input systems. They modeled the problem as a continuous-time zero-sum game. The study showed new results and creates a least-squares-based algorithm for a practical solution. The proposed algorithm is applied to the RTAC nonlinear benchmark problem. Zhou et al. The model is based on the zero-sum game between two phases. The two phases are training phase and transmission phase. This study is about optimal energy allocation between these two phases.

The study proves the presence of NE for fixed training length. Finally, it discusses channel state information. Tan et al. They used game theory approach for fair sub-carriers allocation and power allocation. The sub-carrier allocation and power allocation are based on colonel blotto game. The secondary users allocate budget wisely to transmit power to win sub-carriers. Power allocation and budget allocation are strategies used for fair sharing among secondary users. This paper proposed algorithms and conditions for the presence of unique NE.

Finally, the results are validated through simulation. Belmega et al. In these channels transmitters and receiver have many antennas. The study gives unique Nash equilibrium. It also gives best power allocation policies. The paper discussed two different games. In the first game, the users can adapt their temporal power allocation to their decoding rank at the receiver. The other is to optimize their spatial power allocation between their transmit antennas. Finally, results are shown via simulation.

In the next section, we will classify games in tabular structures. Then will discuss some open problems. We discussed game theory and its applications in different domains by exploring different papers. We described how game theory models strategic and complex interactions of self-interested agents. We also proposed a general taxonomy of games, based on the types of game representation.

Then we classify games according to these representation types. We have seen different games while reviewing literature. Such as Markov games, Zero-sum game, Stochastic game, Bayesian games etc. These are actually different classes of games having different properties. We summarized different games, by their different types. See Table 3. The legend used in the table is summarized in Table 4. We also summarized games discussed in different papers according to representation forms.

See Table 5. We have noted that while researchers applied game theory in different domains, there is still need to further exploit game theory in the modeling of complex systems research. In computer science, there is also a need to apply game theory in the domain of resource allocation algorithms such as in clouds, Internet of Things, Cyber physical systems, and others. Cake Cutting and Colonel Blotto are quite possibly good game-theoretic resource allocation models and can thus be used in such domains.

However, they have not previously been used much in these areas. Furthermore, fair allocation is still a complex task in distributed systems. With the advent of mobile, pervasive computing, and cloud-based systems, practical distributed computing requires the resolution of such dilemmas on a regular basis. In other words, there is a growing need to use game theory for practical applications in the technological domains rather than restrict it to purely theoretical applications and those too, limited to very specific and niche areas of research.