In this paper, we describe a new algorithm based on game theory for minimizing the average power of a circuit during binding in behavioral synthesis. The problem is formulated as an auction based non-cooperative finite game for which a solution is proposed based on the Nash equilibrium. 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. The operations are bound to the modules such that the total power consumption is minimized. Further, the techniques of functional unit sharing, path balancing and register assignment are incorporated within the binding algorithm for power reduction. The proposed algorithm yields power reduction without any increase in area or delay overhead. Experimental results indicate that the proposed game theoretic solution for binding yields an improvement of 13.9% over the linear programming (LP) method in [16].