Economic Perspectives I

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Better Performance Via Bayesian Updating

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

Consider the simulation to your left. Each of the three Agents in the left column picks one of the four possible actions in the right column at every other step. Only one of the four actions is consistent with the world's true state, and will lead an Agent to non-zero payoffs (this action is marked with a T to the circle's right). On the other hand, choosing one of the three "F" actions is a waste of effort for either of the Agents. In what way does information make a difference in their performance?

Consistent with the previous slide's discussion, each Agent maintains a probability distribution over the set of given possibilities. Graphically, the distribution is represented by the Agent's pie circle. For instance, according to the Informed Agent's belief, the probability that the Blue Action is the "true" action is proportional to the size of the blue slice in the Agent's pie. Each agent, then, will choose the action with the largest pie slice in her circle - the one most likely to be beneficial.

Press the "Go" button several times to see the simulation progress. Note that the Omniscient Agent always has perfect knowledge of the world state, which is reflected in her optimal performance. The Informed Agent receives a signal from the Omniscient Agent by connecting to her at every other step. This signal often improves the Agent's probability distribution, which translates into better average performance than the Uninformed Agent.

The Informed Agent gets only 5 updates from the Omniscient Agent to learn which one is the "true" action. That's because during every fifth update cycle the world state changes randomly, and the Informed Agent starts with the original, unbiased probability distribution.

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