As the availability of distributed generation and storage increases, market mechanisms are needed for local energy grids that reflect the changing distribution of market power among participants. These networks are likely to transition to a mixed model, with distributed resources backed by central or microgrid-scale generation assets. This paper introduces a framework for the design of multiple time scale markets for economic dispatch in which, at each time scale, producers, consumers, and producer-consumers are represented by agents that participate via a communication network in a multi-round double auction. The market framework enables diverse valuation of energy at different spatio-temporal scales, and the auction mechanism allows participants to equip their agents with adaptive parameterized strategies. By design, the mechanism enables compensation for uncertainty at coarse time scales by participation in markets at finer scales. The mechanism also admits offer (bid/ask) functions that generalize the traditional single limit order (price-quantity pair), so that participants can design offers to buy or sell that reflect their valuations of energy for different purposes, such as heating at subsistence and comfort levels. Performance measures are introduced that capture the ability of participants to achieve their economic objectives, and simulations demonstrate the effect on performance of different strategies.