Design and Mathematical Analysis of Agent-based Systems

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Design and Mathematical Analysis of Agent-based
Systems

• Wang Yuanshi
• (Based on 1)

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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.

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Assumptions

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

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Mathematical Model
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Efficiency Function
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Steady State of the Model
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Efficiency of the Steady State
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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.

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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.