Plug-in hybrid electric vehicles (PHEVs) will constitute a key element in the emerging smart grid system. In this paper, the complex decision making processes of a number of PHEV groups seeking to sell part of their stored energy in a power market are studied using noncooperative games and double auctions. In particular, a noncooperative game is formulated between the PHEV groups. In this game, each PHEV group can make a decision on the maximum amount of energy surplus that it is willing to sell so as to maximize a utility function that captures the tradeoff between the economical benefits from energy trading and the associated costs. The trading price governing the energy exchange market between the PHEVs and the smart grid network is determined using a strategy-proof double auction. For solving the game, an algorithm based on best response dynamics is proposed using which the PHEV groups can reach a Nash equilibrium point. Simulation results show how our approach allows the PHEV groups to act strategically while improving the average utility achieved per PHEV group of up to 100.2% relative to a greedy algorithm.