In this paper, the problem of energy trading between smart grid prosumers that can simultaneously consume and produce energy is studied. The problem is formulated as a noncooperative game between prosumers whose goal is to meet their energy demands at minimum cost by optimally utilizing their storage units and renewable (wind) energy sources. In this game, each prosumer will declare the amount of energy that will be sold or bought to maximize a utility function that captures the tradeoff between the profits gained from selling energy and the penalty incurred for failing to meet the declared amount, due to the stochastic nature of wind energy. The proposed game explicitly accounts for each prosumer's subjective perceptions using the framework of prospect theory (PT). In particular, a prosumer's perception of the probability of its possible profits from trading energy is captured via the weighting effect. In addition, the prosumer's valuation of its gains and losses with respect to its own preferences is captured via the so-called framing effect. To find the equilibrium of this game, a best response algorithm is proposed. Simulation results show the difference in prosumer behavior using traditional game-theoretic and prospect-theoretic analysis. In particular, the results show that probability weighting increases the sensitivity of the prosumers to penalties. Moreover, under PT, a prosumer tends to sell less energy compared to a conventional game-theoretic scenario.