Geodesic
Reduction of searching competetive equillibrium to the minimax problem in application to different network problems
Matematičeskoe modelirovanie, Tome 27 (2015) no. 12, pp. 121-136

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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.
Keywords: competitive equilibrium, evolutionary game, sadle point, multi-level optimization, macro balance. 
@article{MM_2015_27_12_a8,
     author = {A. V. Gasnikov},
     title = {Reduction of searching competetive equillibrium to the minimax problem in application to different network problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {27},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_12_a8/}
}
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A. V. Gasnikov. Reduction of searching competetive equillibrium to the minimax problem in application to different network problems. Matematičeskoe modelirovanie, Tome 27 (2015) no. 12, pp. 121-136. http://geodesic.mathdoc.fr/item/MM_2015_27_12_a8/