In this work we essentially reinterpreted the Sieczka-Ho{l}yst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbor
s to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the SH model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.
