Remarks on quantum duopoly schemes

Frąckiewicz, Piotr

doi:10.1007/s11128-015-1163-1

Cited by 45 publications

(39 citation statements)

References 24 publications

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“…The scheme, originally designed for Cournot duopoly, enables the players to avoid an inefficient Nash equilibrium by means of quantum resources. Moreover, it preserves the uniqueness of the solution [10,22]. In essence, the result has been proved for a specific Cournot duopoly example.…”

Section: Introductionmentioning

confidence: 81%

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Quantum Approach to Cournot-type Competition

Frąckiewicz

2017

Int J Theor Phys

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The aim of this paper is to investigate Cournot-type competition in the quantum domain with the use of the Li-Du-Massar scheme for continuous-variable quantum games. We derive a formula which, in a simple way, determines a unique Nash equilibrium. The result concerns a large class of Cournot duopoly problems including the competition, where the demand and cost functions are not necessary linear. Further, we show that the Nash equilibrium converges to a Pareto-optimal strategy profile as the quantum correlation increases. In addition to illustrating how the formula works, we provide the readers with two examples.

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Section: Introductionmentioning

confidence: 81%

“…The following example gives us a look at how (19) simplifies the analysis required to find Nash equilibria compared to [10,22].…”

Section: Proposition 1 Suppose That the Demand Functionmentioning

confidence: 99%

Quantum Approach to Cournot-type Competition

Frąckiewicz

2017

Int J Theor Phys

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“…In [32] we discussed two well-known quantum duopoly schemes [20,33]. We pointed out that under some condition the Li-Du-Massar scheme [20] appears to be more reasonable.…”

Section: Quantum Bertrand Duopolymentioning

confidence: 99%

“…However, the correlation between prices can be defined in many different ways. In paper [32], we introduced a simplified model that correlate the players choices x 1 , x 2 ∈ [0, ∞) in the following way:…”

Section: Bertrand Duopoly With Fully Correlated Quantitiesmentioning

confidence: 99%

Quantum approach to Bertrand duopoly

FraźCkiewicz

Sładkowski

2016

Quantum Inf Process

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The aim of the paper is to study the Bertrand duopoly example in the quantum domain. We use two ways to write the game in terms of quantum theory. The first one adapts the Li-Du-Massar scheme for the Cournot duopoly. The second one is a simplified model that exploits a two qubit entangled state. In both cases, we focus on finding Nash equilibria in the resulting games. Our analysis allows us to take another look at the classic model of Bertrand.

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“…A rich literature applies the Li-Du-Massar scheme to the Cournot dupoly problems [14], [15], [16], [17], the Stackelberg duopoly [23], [18], [19], [20] and the Bertrand duopoly examples [21], [22], [27] The existing results motivate further study rather than exhaust the subject. Our previous work [17] shows that the quantum Cournot duopoly given by a piecewise function requires a best reply analysis to determine Nash equilibria of the game. This method found further application in the quantum Bertrand duopoly (with discontinuous payoff functions) [27].…”

Section: Introductionmentioning

confidence: 99%