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In this paper, we describe a new methodology based on game theory for minimizing the average power of a circuit during scheduling and binding in behavioral synthesis. The problems are formulated as auction-based noncooperative finite games for which solutions are proposed based on the Nash equilibrium. In the scheduling algorithm, a first-price sealed-bid auction approach is used while, for the binding algorithm, each functional unit in the datapath is modeled as a player bidding for executing an operation with the estimated power consumption as the bid. Further, the techniques of functional unit sharing, path balancing, and register assignment are incorporated within the binding algorithm for power reduction. The combined scheduling and binding algorithm is formulated as a single noncooperative auction game with the functional units in the datapath modeled as players bidding for executing the operation in a particular control cycle. The proposed algorithms yield power reduction without any increase in area overhead and only a slight increase in the latency for some of the benchmark circuits. Experimental results indicate that the proposed game theoretic solution for binding yields an improvement of 13.9% over the linear programming (LP) method, while the scheduling and the combined scheduling and binding algorithms yield average improvements of 6.3% and 11.8%, respectively, over the integer-linear programming (ILP) approach.