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Smart Grids components include scalable metering, energy prediction (both production and consumption) and pricing. One of their goals consists to attract consumers to use green energy, to promote periods of low consumption and to dissuade customers from using their greedy devices during peak periods. The objective consists to determine the optimal suggested prices by the energy operator and the optimal demands of consumers. In this paper, we propose a theoretical model based on Stackelberg game to adjust prices of green energy. The proposed game is composed by a leader represented by the operator, and multiple followers represented by consumers. A Nash/Stackelberg equilibrium solution is found. Performance results confirm the uniqueness of Nash equilibrium and that a "best reply" dynamics for the repeated game converges to this equilibrium. Keywords: Smart grids, game theory, optimization, dynamic pricing 1. Introduction To meet the future power demand and the aim to reduce 2 emissions designers of the next generation of electric power, distribution grid initiate a large research and technological action under the "Smart Grid" banner that starts to tackle some of the following issues:

A game theory approach with dynamic pricing to optimize smart grid operation