Nash Equilibrium to Competitive Equilibrium Mechanisms Design: Subsidization and Punishment

Due to the small number of participants in realistic cases, the Nash equilibrium generated by an oligopolistic market is more appropriate for depicting the actual energy market than the competitive equilibrium generated by a competitive market. However, the market efficiency decreases when the Nash equilibrium is used rather than the competitive equilibrium because of the strategic behaviors of the participants. In this paper, we propose two new mechanisms (subsidization and punishment) for each generator, both of which drive the Nash equilibrium to the competitive equilibrium in heterogeneous oligopolistic energy markets with a uniform pricing mechanism. Under the two proposed mechanisms, the equivalence of the Nash equilibrium and the competitive equilibrium is strictly proven. Furthermore, we apply a distributed algorithm to numerically confirm that both mechanisms perfectly eliminate the market efficiency loss. Finally, these two mechanisms are applied to the energy market under three different stages of development. Simulation results illustrate that the additional costs caused by the mechanisms converge to a low value and that the subsidization mechanism slightly outperforms the punishment mechanism.