An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

摘要

We propose a novel method to find Nash equilibria in games with binarydecision variables by including compensation payments andincentive-compatibility constraints from non-cooperative game theory directlyinto an optimization framework in lieu of using first order conditions of alinearization, or relaxation of integrality conditions. The reformulationoffers a new approach to obtain and interpret dual variables to binaryconstraints using the benefit or loss from deviation rather than marginalrelaxations. The method endogenizes the trade-off between overall (societal)efficiency and compensation payments necessary to align incentives ofindividual players. We provide existence results and conditions under whichthis problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibriumproblem with binary on-off decisions. This illustrative example shows that ourapproach yields an exact solution to the binary Nash game with compensation. Wecompare different implementations of actual market rules within our model, inparticular constraints ensuring non-negative profits (no-loss rule) andrestrictions on the compensation payments to non-dispatched generators. Wediscuss the resulting equilibria in terms of overall welfare, efficiency, andallocational equity.