We propose a novel method to fi nd Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation off ers a new approach to obtain and interpret dual variables to binary constraints using the benefi t or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-o ff decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare diff erent implementations of actual market rules within our model, in particular constraints ensuring non-negative pro fits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity.
Citation
Department of Civil Engineering & Johns Hopkins Systems Institute, Johns Hopkins University, Baltimore, MD (2015)