One method for computing the Pareto-optimal Nash equilibrium in bimatrix game

Kudryavtsev, Konstantin; Zhukovskiy, Vladislav I.; Stabulit, Irina

doi:10.1109/cnsa.2017.7973978

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…; z * ðÞ exists in the antagonistic game (9) (i.e., the condition (10) holds), then the minimax strategy z * is a PoNE strategy profile for game (1) [14].…”

Section: Theorem 1 If a Saddle Point X Omentioning

confidence: 99%

“…In (14), a decision-maker chooses a strategy profile ν Á ðÞ∈ N to simultaneously maximize all components of the vector criterion f ν ðÞ¼ f 1 ν ðÞ ; …; f N ν ðÞ ÀÁ…”

Section: Existence Of Pone Strategy Profile In Mixed Strategiesmentioning

confidence: 99%

“…Definition 5. A strategy profile ν P Á ðÞ∈ N is called Pareto optimal for the N-criterion problemΓ υ from (14) if for any ν Á ðÞ∈ N the system of inequalities…”

Section: Existence Of Pone Strategy Profile In Mixed Strategiesmentioning

confidence: 99%

See 2 more Smart Citations

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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“…; z * ðÞ exists in the antagonistic game (9) (i.e., the condition (10) holds), then the minimax strategy z * is a PoNE strategy profile for game (1) [14].…”

Section: Theorem 1 If a Saddle Point X Omentioning

confidence: 99%

“…In (14), a decision-maker chooses a strategy profile ν Á ðÞ∈ N to simultaneously maximize all components of the vector criterion f ν ðÞ¼ f 1 ν ðÞ ; …; f N ν ðÞ ÀÁ…”

Section: Existence Of Pone Strategy Profile In Mixed Strategiesmentioning

confidence: 99%

See 1 more Smart Citation

Pareto Optimality and Equilibria in Noncooperative Games

Zhukovskiy¹,

Kudryavtsev²

2020

Multicriteria Optimization - Pareto-Optimality and Threshold-Optimality

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New algorithm for checking Pareto optimality in bimatrix games

Kicsiny

Varga

2022

Ann Oper Res

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Bimatrix games have had theoretical importance and important applications since the very beginning of game theory to date. Pareto optimal strategy vectors represent a reasonable and frequently applied solution concept (basically in the cooperative approach). Particularly, it often arises whether a non-cooperative solution can be improved in cooperative sense, i.e. it is Pareto optimal or not. However, in concrete cases it may be hard to determine the Pareto optimal strategy vectors or at least check the Pareto optimality of a given strategy vector. In the present paper, the Pareto optimality of the strategy pairs in general n × m ($$n = 2,3, \ldots$$ n = 2 , 3 , … ; $$m = 2,3, \ldots$$ m = 2 , 3 , … ) bimatrix games is studied. First of all an elementary proof is provided for a theorem, which makes the proposed Pareto optimality checking algorithm simpler. Then a nonlinear transform is proposed, which makes the algorithm even more convenient in the important case of 2 × 2 bimatrix games (and for certain other cases). Two numerical examples present the practical applicability of the checking algorithm. The problem of 2 × 2 bimatrix games can be solved even by hand. For larger games, numerous computational tools are available in the practice to apply the checking algorithm in exact or at least approximate way.

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One method for computing the Pareto-optimal Nash equilibrium in bimatrix game

Cited by 2 publications

References 3 publications

Pareto Optimality and Equilibria in Noncooperative Games

Pareto Optimality and Equilibria in Noncooperative Games

New algorithm for checking Pareto optimality in bimatrix games

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