1. Design and Mathematical Analysis of Agent-based Systems Wang Yuanshi (Based on [1])

2. Backgrounds Consider a system where each agent is given a task to obtain goods at the lowest price. Forming coalitions to buy goods in bulk is a good strategy to save money.

3. Assumptions 1.Dispersion 2.Aggregation 3.Agents are homogeneous. 4.The number of agents remains unchanged. 5.Agents are mobile and self-interested.

4. Mathematical Model

5. Efficiency Function

6. Steady State of the Model

7. Efficiency of the Steady State

8. Open Problems It is as yet unresolved whether the equilibrium state is stable. The model should be made more realistic by incrementally relaxing the assumptions and adding more realistic agent behaviors. Some assumptions have no effect on the model.

9. References 1.Kristina Lerman "Design and Mathematical Analysis of Agent-based Systems," Lecture Notes in Artificial Intelligence (LNAI) 1871, p. 222 ff., Springer-Verlag, Berlin Heidelberg, 2001. 2.Kristina Lerman and Aram Galstyan (2001) "A General Methodology for Mathematical Analysis of Multi- Agent Systems," USC Information Sciences Technical Report ISI-TR-529.