Multiagent Systems

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of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 354/731 5. Nets and coalitions 2. Four Types of Nets Proof. Consider O contracts (as fourth type). One task and 2 agents: T 1 = {t 1 }, T 2 = ∅. c 1 (∅) = 0, c 1 ({t 1 }) = 2, c 2 (∅) = 0, c 2 ({t 1 }) = 1. The O contract of moving t 1 would decrease global cost by 1. No C-, S-, or M-contract is possible. To show the same for C or S contracts, two agents and two tasks suffice. For M-contracts 3 agents and 3 tasks are needed.
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 355/731 5. Nets and coalitions 2. Four Types of Nets Theorem 5.14 (O-, C-, S-, M- Global Optima) There are instances of the task allocation problem where no IR sequence from the initial task allocation to the optimal one exists using O-, C-, S-, and M- contracts. Proof. Construct cost functions such that the deal where agent 1 gives one task to agent 2 and agent 2 gives 2 tasks to agent 1 is the only one increasing welfare. This deal is not possible with O-, C-, S-, or M-contracts.
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9. Agents based on FOL 1. First Ord
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Situation independent functions dec
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9. Agents based on FOL 7. Reference
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