An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem

33 Pages Posted: 8 May 2015

See all articles by Daniel Huppmann

Daniel Huppmann

International Institute for Applied Systems Analysis (IIASA)

Sauleh Siddiqui

Johns Hopkins University

Date Written: April 2015

Abstract

We propose a novel method to find 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 offers a new approach to obtain and interpret dual variables to binary constraints using the benefit 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-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (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.

Keywords: binary Nash game, non-cooperative equilibrium, compensation, incentive compatibility, electricity market, power market, uplift payments

JEL Classification: C72, C61, L13, L94

Suggested Citation

Huppmann, Daniel and Siddiqui, Sauleh, An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem (April 2015). DIW Berlin Discussion Paper No. 1475, Available at SSRN: https://ssrn.com/abstract=2603231 or http://dx.doi.org/10.2139/ssrn.2603231

Daniel Huppmann (Contact Author)

International Institute for Applied Systems Analysis (IIASA) ( email )

Schlossplatz 1
Laxenburg, A-2361
Austria

Sauleh Siddiqui

Johns Hopkins University ( email )

Baltimore, MD 20036-1984
United States

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