In this paper we describe aspects of a market model for Grid computing. In particular we concentrate on Grid computing provided by a peer-to-peer network architecture. In this network nodes can either buy or sell computing power in exchange for money. Building on previous publications we develop a mathematical market model using Markov chains. The behaviour of each agent in the market is described by a Markov chain of decisions on buying, selling or holding. Considering the contributions of all agents, we calculate the global Markov chain of the market state as a whole, by making use of a concept of market pressure that reduces the state space of the entire market model. We show that the Markov chain model describes the market behaviour seen in a simulation extremely well. In a similar way to other perishable commodity markets like fish and electricity, we also provide a model for trading future contracts on the purchase and sale of computing power in this market. Using Markov Decision Processes we derive an optimal trading strategy. This work introduces a pioneer mathematical model for future global peer-to-peer Grid computing architectures like MaGoG (Middleware for activating the Global open Grid), where we have derived a global transition probability matrix that determines the behaviour of the market by summing up the contributions of different kinds of market participants.
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