About reduction of searching competetive equillibrium to the minimax problem in application to different network problems

TL;DR

This paper demonstrates that multistage traffic equilibrium models and their economic generalizations can be reformulated as population games with a minimax structure, simplifying the analysis of competitive equilibria.

Contribution

It introduces a novel approach linking traffic and economic equilibrium models to minimax problems, enabling new analytical methods.

Findings

Equilibrium models can be viewed as population games with minimax structure.

Reformulation simplifies analysis of competitive and Nash equilibria.

Provides a unified framework for traffic and economic models.

Abstract

In the paper we show that an important class of multistage traffic equillibrium models (including correspondence matrix calculation, traffic assignment problem etc) and their economic generalizations can be considered as proper population games with the minimax structure of equillibriums. This is not trivial because at the first sight we have to consider competetive (Valras) equilibrium and Nash-Vardroop equillibrium.