Fixed point theorem for simple quantum strategies in quantum market games

A simple but nontrivial class of the quantum strategies in buyingselling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal profits in such the games is considered. The entangled merchants hypothesis is proposed. 1 Projective geometry approach to profits Half thousand years ago Fra Luca Pacioli, a teacher of Leonardo da Vinci set standards of Venice accounting (i.e. the double accounting) and for the theory of perspective. In the author opinion this is not accidental because projective geometry approach forms a natural language of description of the market reality. Let us consider the simplest possible market event of exchanging two goods which we would call the asset and the money and denote them by Θ and $, respectively. Let VΘ and V$ denote some given amounts of the asset and the money, respectively. If the assets are exchanged in the proportion V$ :VΘ then in the context of selling processes we call the logarithmic quotation for the asset Θ p := ln (V$)− ln (VΘ) (1)