We study two problems directly resulting from organizational decentralization of the grid. Firstly, the problem of fair scheduling in systems in which the grid scheduler has complete control of processors' schedules. Secondly, the problem of fair and feasible scheduling in decentralized case, in which the grid scheduler can only suggest a schedule, which can be later modified by a processor's owner. Using game theory, we show that scheduling in decentralized case is analogous to the prisoner's dilemma game. Moreover, the Nash equilibrium results in significant performance drop. Therefore, a strong community control is required to achieve acceptable performance.