Quantum Approach to Cournot-type Competition

Abstract

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.

Quantum Games with Unawareness with Duopoly Problems in View

“…It follows from Proposition 1 the result predicted by an ENE in is a Nash equilibrium in . The Cournot duopoly game has the unique Nash equilibrium (see, for example, [ 24 ]). As a result, Formula ( 40 ) is true for .…”

On subgame perfect equilibria in quantum Stackelberg duopoly

“…For the convenience of the reader we repeat the relevant material from [13], [27], [28] and [29] in order to make our exposition self-contained. Let |00 be the initial state and J(γ) = e −γ(a † A a † B −a A a B ) be a unitary operator, where γ ≥ 0 and a † i (a i ) represents the creation (annihilation) operator of electromagnetic field i.…”

Nonlinear dynamics in a heterogeneous quantum Cournot duopoly game with isoelastic demand

“…In the research of quantum oligopoly games, Li et al first proposed a "minimal" quantization rules to generate the quantization version of the classical Cournot duopoly game [8]. After that, a number of researches applied the Li et al's quantization approach to study Cournot duopoly [1,6,[9][10][11], Bertrand duopoly [7,12,13], Stackelberg duopoly games [14][15][16][17][18].…”