The goal of the research was to observe and analyze self-organization patterns in Multi-Agent Systems (MAS) by modeling basic economic relationships between agents. The paper describes the worked-out MAS including the example of a production cycle and used economic rules. A special focus is put on behavior rules and decision systems of an individual agent as product advertising, price & purchase negotiations, deals in the context of limited resources and time constraints to make a decision. The MAS was implemented in a dedicated C#-based environment and a number of simulations were carried out. The paper reports some of recorded self-organization patterns and their dynamics over time in terms of their spatial arrangement or mutual relations (e.g.: bargain price, market shares, etc.), and provides their analysis and discussion.