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Lecture Multiagent systems - Chapter 6: Multiagent interactions

The most important lesson of this chapter - and perhaps one of the most important lessons of multiagent systems generally - is that when faced with what appears to be a multiagent domain, it is critically important to understand the type of interaction that takes place between the agents. To see what I mean by this, let us start with some notation. | LECTURE 6: MULTIAGENT INTERACTIONS An Introduction to MultiAgent Systems http://www.csc.liv.ac.uk/~mjw/pubs/imas What are Multiagent Systems? 6- MultiAgent Systems Thus a multiagent system contains a number of agents which interact through communication are able to act in an environment have different “spheres of influence” (which may coincide) will be linked by other (organizational) relationships 6- Utilities and Preferences Assume we have just two agents: Ag = {i, j} Agents are assumed to be self-interested: they have preferences over how the environment is Assume W = {w1, w2, }is the set of “outcomes” that agents have preferences over We capture preferences by utility functions: ui = W ú uj = W ú Utility functions lead to preference orderings over outcomes: w ši w’ means ui(w) $ ui(w’) w ™i w’ means ui(w) > ui(w’) 6- What is Utility? Utility is not money (but it is a useful analogy) Typical relationship between utility & money: 6- Multiagent . | LECTURE 6: MULTIAGENT INTERACTIONS An Introduction to MultiAgent Systems http://www.csc.liv.ac.uk/~mjw/pubs/imas What are Multiagent Systems? 6- MultiAgent Systems Thus a multiagent system contains a number of agents which interact through communication are able to act in an environment have different “spheres of influence” (which may coincide) will be linked by other (organizational) relationships 6- Utilities and Preferences Assume we have just two agents: Ag = {i, j} Agents are assumed to be self-interested: they have preferences over how the environment is Assume W = {w1, w2, }is the set of “outcomes” that agents have preferences over We capture preferences by utility functions: ui = W ú uj = W ú Utility functions lead to preference orderings over outcomes: w ši w’ means ui(w) $ ui(w’) w ™i w’ means ui(w) > ui(w’) 6- What is Utility? Utility is not money (but it is a useful analogy) Typical relationship between utility & money: 6- Multiagent Encounters We need a model of the environment in which these agents will act agents simultaneously choose an action to perform, and as a result of the actions they select, an outcome in W will result the actual outcome depends on the combination of actions assume each agent has just two possible actions that it can perform, C (“cooperate”) and D (“defect”) Environment behavior given by state transformer function: 6- Multiagent Encounters Here is a state transformer function: (This environment is sensitive to actions of both agents.) Here is another: (Neither agent has any influence in this environment.) And here is another: (This environment is controlled by j.) 6- Rational Action Suppose we have the case where both agents can influence the outcome, and they have utility functions as follows: With a bit of abuse of notation: Then agent i’s preferences are: “C” is the rational choice for i. (Because i prefers all outcomes that arise through C over all outcomes that arise .