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Design and Mathematical Analysis of Agent-based Systems

This paper investigates a system of self-interested agents tasked with purchasing goods at minimal costs. By forming coalitions, agents can buy in bulk for savings. We assume homogeneous agents, constant agent numbers, and mobility, leading to a mathematical model evaluating efficiency in a steady state. Key open problems include the stability of equilibrium states and the need for more realistic modeling by adjusting assumptions and agent behaviors. The findings contribute to understanding agent-based systems, with references to previous methodologies and analyses in the field.

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Design and Mathematical Analysis of Agent-based Systems

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  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 Dispersion Aggregation Agents are homogeneous. The number of agents remains unchanged. 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 • 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. • Kristina Lerman and Aram Galstyan (2001) "A General Methodology for Mathematical Analysis of Multi-Agent Systems," USC Information Sciences Technical Report ISI-TR-529.

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