Publication

Reaching Correlated Equilibria Through Multi-agent Learning

Boi Faltings, Ludek Cigler
2011
Conference paper
Abstract

Many games have undesirable Nash equilibria. For exam- ple consider a resource allocation game in which two players compete for an exclusive access to a single resource. It has three Nash equilibria. The two pure-strategy NE are effi- cient, but not fair. The one mixed-strategy NE is fair, but not efficient. Aumann’s notion of correlated equilibrium fixes this problem: It assumes a correlation device which suggests each agent an action to take. However, such a “smart” coordination device might not be available. We propose using a randomly chosen, “stupid” in- teger coordination signal. “Smart” agents learn which action they should use for each value of the coordination signal. We present a multi-agent learning algorithm which con- verges in polynomial number of steps to a correlated equilib- rium of a wireless channel allocation game, a variant of the resource allocation game. We show that the agents learn to play for each coordination signal value a randomly chosen pure-strategy Nash equilibrium of the game. Therefore, the outcome is an efficient correlated equilibrium. This CE be- comes more fair as the number of the available coordination signal values increases. We believe that a similar approach can be used to reach efficient and fair correlated equilibria in a wider set of games, such as potential games.

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Related concepts (32)
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.
Intelligent agent
In artificial intelligence, an intelligent agent (IA) is an agent acting in an intelligent manner; It perceives its environment, takes actions autonomously in order to achieve goals, and may improve its performance with learning or acquiring knowledge. An intelligent agent may be simple or complex: A thermostat or other control system is considered an example of an intelligent agent, as is a human being, as is any system that meets the definition, such as a firm, a state, or a biome.
Multi-agent system
A multi-agent system (MAS or "self-organized system") is a computerized system composed of multiple interacting intelligent agents. Multi-agent systems can solve problems that are difficult or impossible for an individual agent or a monolithic system to solve. Intelligence may include methodic, functional, procedural approaches, algorithmic search or reinforcement learning. Despite considerable overlap, a multi-agent system is not always the same as an agent-based model (ABM).
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