Description of the Bluffing Phenomenon in the Untrusted Seller–Buyer Relationship via the Wigner Function of the q-Deformed Quantum Harmonic Oscillator Model

Abstract

The $q$ -deformed quantum harmonic oscillator model is applied to the description of the untrusted seller–buyer relationship. We assumed that the demand law by the buyer is described through the square modulus of the wavefunctions of the $q$ -oscillator model in the position representation, whereas the supply law by the seller is described through the square modulus of the wavefunctions in the momentum representation. Thus, their untrusted relationship is described through the $q$ -oscillator Wigner function of the stationary states in terms of the Al Salam-Chihara polynomials. As an example, we study the first excited state and show that the finite-difference differentiation parameter $h$ or the deformation parameter $q$ generated through it can be considered as a parameter defining the level of the bluffing phenomenon in this untrusted relationship.

JEL Classifications: C02, D01, D11, D46, D58, D81

Keywords

Bluffing phenomenon Wigner function q-deformed oscillator Giffen goods orthogonal polynomials

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