Vladislav I. Zhukovskiy, Konstantin N. Kudryavtsev, “Mathematical foundations of the Golden Rule. I. Static variant”, Mat. Teor. Igr Pril., 2015, Volume 7, Issue 3,Pages <nobr>16

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Mathematical foundations of the Golden Rule. I. Static variant

Vladislav I. Zhukovskiy^a, Konstantin N. Kudryavtsev^b

^a Moscow State University
^b South Ural State University

Abstract: The Berge equilibrium concept was suggested by Russian mathematician K. Vaisman in 1994. In the presented paper, we offer to use this concept as a mathematical model of the Golden Rule. The Berge–Pareto equilibrium is formalized, sufficient conditions for the existence of the equilibrium are found. For mixed strategies, the existence of the equilibrium is proved.

Keywords: non-cooperative game, Berge equilibrium, Pareto maximum.

UDC: 519.833
BBK: 91АД, 49Л35