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

TL;DR

This paper introduces an exact optimization-based method for finding Nash equilibria in binary decision games with compensation, applied to power markets, enabling precise analysis of market rules and incentives.

Contribution

It presents a novel reformulation that directly incorporates compensation and incentive constraints into an optimization framework for binary games, providing exact solutions and dual variable interpretation.

Findings

The method yields exact solutions for binary Nash games with compensation.

Application to power markets demonstrates the approach's effectiveness.

Analysis of market rules impacts on welfare and efficiency.

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.