Managing Price Uncertainty in Prosumer-Centric Energy Trading: A\n Prospect-Theoretic Stackelberg Game Approach

In this paper, the problem of energy trading between smart grid prosumers,\nwho can simultaneously consume and produce energy, and a grid power company is\nstudied. The problem is formulated as a single-leader, multiple-follower\nStackelberg game between the power company and multiple prosumers. In this\ngame, the power company acts as a leader who determines the pricing strategy\nthat maximizes its profits, while the prosumers act as followers who react by\nchoosing the amount of energy to buy or sell so as to optimize their current\nand future profits. The proposed game accounts for each prosumer's subjective\ndecision when faced with the uncertainty of profits, induced by the random\nfuture price. In particular, the framing effect, from the framework of prospect\ntheory (PT), is used to account for each prosumer's valuation of its gains and\nlosses with respect to an individual utility reference point. The reference\npoint changes between prosumers and stems from their past experience and future\naspirations of profits. The followers' noncooperative game is shown to admit a\nunique pure-strategy Nash equilibrium (NE) under classical game theory (CGT)\nwhich is obtained using a fully distributed algorithm. The results are extended\nto account for the case of PT using algorithmic solutions that can achieve an\nNE under certain conditions. Simulation results show that the total grid load\nvaries significantly with the prosumers' reference point and their\nloss-aversion level. In addition, it is shown that the power company's profits\nconsiderably decrease when it fails to account for the prosumers' subjective\nperceptions under PT.\n