Mathematical foundations of the Golden Rule. I. Static case

Zhukovskiy, Vladislav I.; Kudryavtsev, Konstantin

doi:10.1134/s0005117917100149

Cited by 14 publications

(2 citation statements)

References 6 publications

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“…As an application, this chapter establishes the existence of the Pareto-optimal Nash equilibrium (PoNE) strategy profile in the class of mixed strategies (see Assertion 1). Similar results were obtained by the authors for the Pareto-optimal Berge equilibrium in [4].…”

Section: Introductionsupporting

confidence: 90%

Pareto Optimality and Equilibria in Noncooperative Games

Zhukovskiy¹,

Kudryavtsev²

2020

Multicriteria Optimization - Pareto-Optimality and Threshold-Optimality

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This chapter considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest of the Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the noncooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto-optimal Nash equilibria (PoNE) in mixed strategies is proven.

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Section: Introductionsupporting

confidence: 90%

Pareto Optimality and Equilibria in Noncooperative Games

Zhukovskiy¹,

Kudryavtsev²

2020

Multicriteria Optimization - Pareto-Optimality and Threshold-Optimality

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“…from Alexander Dumas's novel "The Three Musketeers". Another interpretation of the Berge equilibrium is [8] the Golden Rule of morality: "Treat others the way you want to be treated". The development of the Berge equilibrium concept is described in details in the review [9].…”

Section: Introductionmentioning

confidence: 99%

Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

Kudryavtsev

Malkov

2020

Open Computer Science

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The paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

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