The simplest model, with fixed price, was run with 3 sellers and 30 buyers, for a large variety of parameter configurations and initial conditions. The following parameter configuration was chosen to give simple time charts for shop performance and to highlight differences in buyers behavior. Price parameters b, c, and where respectively 1, 1, and 0.3, which corresponds to a price of for a purchased quantity per transaction (according to equation 3), a profit per transaction for the buyer (equ. 2), a critical non-linear parameter (equ. 16) and a profit per transaction for the seller (equ. 4). Our choice of the memory constant of equation (7) is = 0.1. Initial were all 0.
Depending on the value of the non-linear parameter , the two predicted behaviours are observed.