Abstract — In this paper we use game theory to study node behavior in distributed systems. Single stage game of complete information and infinitely repeated game is used to give prescription of node’s behavior. In a single stage game nodes will be non-cooperative, but when the game is infinitely repeated their strategy depends on the discount factor, i.e. the probability for a next round. Using game theory we also model the interaction between a node and the distributed environment as a whole. Keywords — distributed computing, game theory, grid computing, nash equilibrium. I. INTRODUCTION HE need of distributed resources is greater than ever and become more practical with the development of the Internet. The Internet and its current state offers big possibilities, which if they are wisely used they can be of a great importance and relevance of the human kind. As a result there are a wide variety of implemented distributed systems [1]. These distributed systems can offer users computer resources in order to speed up the execution time of a certain complex and time-dependent computer program by distributing it for execution across the CPU’s in the network. Nodes that can accomplish their tasks fast can receive some payment from the network authority. Having this in mind the forthcoming question here is whether for the users (i.e. nodes) it is better to cooperate and give some portion of the program to be executed by the other users. In order to analyze the distributed systems we propose game theory as a mathematical tool [2]. Game theory introduces mathematical background for different analysis of the interactive processes for decision making. This theory enables tools that can leverage the prediction of what might happen in an environment in which there is interaction between agents with conflict Igor Mishkovski, Faculty of Electrotechnics and Information Technology, Skopje, Macedonia (phone: 389-2-3099153; faks: 389-2-3064262; e-mail: igorm@feit.ukim.edu.mk). Sonja Filiposka, Faculty of Electrotechnics and Information Technology (FEIT, Skopje, Macedonia (e-mail: filipos@feit.ukim.edu.mk). Dimitar Trajanov, Faculty of Electrotechnics and Information Technology (FEIT, Skopje, Macedonia (e-mail: mite@feit.ukim.edu.mk). Aksenti Grnarov, SEEU, Tetovo, Macedonia (e-mail: grnarov@mt.net.mk) Ljupco Kocarev, Macedonian Academy for Sciences and Arts, Skopje, Macedonia (e-mail: lkocarev@ucsd.edu). interests, i.e. non-cooperative environment. The traditional applications of Game Theory tries to find out the equilibrium point, i.e. set of strategies in which is almost impossible for the individuals to change the current strategy. This theory became was introduced in [3] and its further development was due to the Nash Equilibrium concept in [4]. The games that were studied during the evolution of this theory were well defined mathematical objects. The games are consisted of players, a set of strategies, and specification of the profits for every combination of the strategies. In this study we analyze the case with two nodes in a single stage static game of complete information and we have found out that for a single stage game the strategy that nodes choose in our model, is not to cooperate, i.e. they execute their task by themselves instead of cooperating and by that they share its tasks with the other nodes. Additionally we extend the model by introducing a discount factor [5] in an infinitely repeated game. We calculate the value that this discount factor must satisfy in order a Trigger strategy [2] to be Nash equilibrium. Additionally we introduce another concept where we try to model the relations between one node and the distributed environment as a whole. The rest of the paper is as follows. In Section 2 we present an introduction to Game Theory an in Section 3 the related work in using a game theory as mathematical model for nodes involvement in distributed systems is presented. Section 4 depicts the single stage game for node participation in distributed systems, while Section 5 extends the game to infinitely repeated game. Section 6 models the interaction between a node and the distributed environment as a whole. Section 7 concludes and presents future work in this field. II. RELATED WORK In recent years Game Theory makes big steps in analysis of the distributed computer systems. In [6] authors show how to derive a unified framework for addressing network efficiency, fairness, utility maximization and pricing strategy for efficient job allocation in mobile grids. Their results show an asymptotically optimal behavior. In [7] Kwok et al. present hierarchical game-theoretic model of the grid, while they focus on the impact of non-cooperation in intra-site job execution mechanisms. Using a novel utility function they derive the Nash equilibrium and optimal strategies. In [8] authors, using Game Theory, Using Game Theory to Analyze Distributed Computing Systems Igor Mishkovski, Sonja Filiposka, Dimitar Trajanov, Aksenti Grnarov and Ljupco Kocarev, Member, IEEE T