Distributed algorithms are gaining increasing research interests in the area of power system optimization and dispatch. Existing distributed power dispatch algorithms (DPDAs) usually assume that suppliers/consumers bid truthfully. However, this article shows the need for DPDAs to consider strategic players and to take account of their behavior deviation from what the DPDAs expect. To address this, we propose a distributed strategy update algorithm (DSUA) on top of a DPDA. The DSUA considers strategic suppliers who optimize their bids in a DPDA, using only the information accessible from a DPDA, that is, price. The DSUA also considers the cases when suppliers update bids alternately or simultaneously. Under both cases, we show the closeness of supplier bids to the Nash equilibrium via game-theoretic analysis as well as simulation.