Disclosed herein are representative embodiments of methods, apparatus, and systems for distributing a resource (such as electricity) using a resource allocation system. One of the disclosed embodiments is a method for operating a transactive thermostatic controller configured to submit bids to a market-based resource allocation system. According to the exemplary method, a first bid curve is determined, the first bid curve indicating a first set of bid prices for corresponding temperatures and being associated with a cooling mode of operation for a heating and cooling system. A second bid curve is also determined, the second bid curve indicating a second set of bid prices for corresponding temperatures and being associated with a heating mode of operation for a heating and cooling system. In this embodiment, the first bid curve, the second bid curve, or both the first bid curve and the second bid curve are modified to prevent overlap of any portion of the first bid curve and the second bid curve.
ACKNOWLEDGMENT OF GOVERNMENT SUPPORT
 This invention was made with Government support under Contract DE-AC05-76RLO1830 awarded by the U.S. Department of Energy. The Government has certain rights in the invention.