Multiagentes

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Introduction Multiagent encounters Examples Summary

Introduction Multiagent encounters Examples Summary

Where are we? Agent-Based Systems
Semester 2, 2006-07 Michael Rovatsos mrovatso@inf.ed.ac.uk Last time . . .
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Agent communication Speech act theory Agent communication languages (KQML/KIF, FIPA-ACL) Interaction Protocols Ontologies for communication Multiagent interactionsToday . . . Lecture 8 – Multiagent Interactions 5th February 2007


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Introduction Multiagent encounters Examples Summary

Introduction Multiagent encounters Examples Summary

Preferences and utilities Game theory Solution concepts

Multiagent interactions


Preferences and utilities
◮ ◮We have looked at agent communication, but not described how it is used in actual agent interactions In itself, communication does not have much effect on the agents Now, we are going to look at interactions in which agents affect each other through their actions Assume agents to have “spheres of influence” that they control in the environment Also, we assume that the welfare (goal achievement,utility) of each agent at least partially depends on the actions of others This part of the lecture will deal with what agents should do in the presence of other agents (which also do stuff)
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We first need an abstract model of interactions Assume O = {o1 , . . . on } a set of possible outcomes (e.g. possible “runs” of the system until final states are reached)A preference ordering ≻i ⊆ O × O for agent i is a total, antisymmetric, transitive relation on O, i.e.
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o ≻i o ′ ⇒ o ′ ≻i o o ≻i o ′ ∧ o ′ ≻ o ′′ ⇒ o ≻i o ′′ ∀o, o ′ ∈ O either o ≻i o ′ or o ′ ≻i o





Such an ordering can be used to express strict preferences of an agent over O (write i if also reflexive, i.e. o i o)

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Introduction Multiagent encounters Examples Summary

Preferences and utilities Game theory Solution concepts

Introduction Multiagent encounters Examples Summary

Preferences and utilities Game theory Solution concepts

Preferences and utilities


Preferences and utilities


Preferences are often expressed through a utility function ui : O → R : ui (o) > ui (o ′ ) ⇔ o≻ o ′ , ui (o) ≥ ui (o ′ ) ⇔ o o′

The utility of money:



Utilities make representing preferences easier because the ordering follows naturally if we use real numbers Often, people falsely associate utility directly with money! Intuitively, the utility of money depends on how much money one already has Therefore, utility does not increase proportionally with monetary wealth
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Empirical evidence suggests utility of money is often very close to logarithm function for humans This shows that utility function depends on agent’s risk aversion attitude (value of additional utility depending on current “wealth”)
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Introduction Multiagent encounters Examples Summary

Preferences andutilities Game theory Solution concepts

Introduction Multiagent encounters Examples Summary

Preferences and utilities Game theory Solution concepts

Multiagent encounters


Example: The Prisoner’s Dilemma






Applying the above to a multiagent setting, we need to consider several agents’ actions and the outcomes they lead to For now, restrict ourselves to two players andidentical sets of actions Abstract architecture: state transformer function becomes τ : Ac × Ac → O where Ac are the actions of each of the two agents Outcome depends on other’s actions! ′ ′ For pairs (a1 , a2 ), (a1 , a2 ) ∈ Ac × Ac we can write
(a1 , a2 )
′ ′ (a1 , a2 ) iff τ (a1 , a2 ) ′ ′ τ (a1 , a2 )

Two men are collectively charged with a crime and held in separate cells, with no way of...
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