Geodesic
Mathematical foundations of the Golden Rule. I. Static variant
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 16-47

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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
Mots-clés : Pareto maximum. 
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     author = {Vladislav I. Zhukovskiy and Konstantin N. Kudryavtsev},
     title = {Mathematical foundations of the {Golden} {Rule.} {I.} {Static} variant},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {7},
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Vladislav I. Zhukovskiy; Konstantin N. Kudryavtsev. Mathematical foundations of the Golden Rule. I. Static variant. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 16-47. http://geodesic.mathdoc.fr/item/MGTA_2015_7_3_a1/