Impressions on Goeree et al (2006)

Title: Social learning with private and common values. Link to the paper.

Authors: Goeree, Palfrey, Rogers

Year published: 2006

Journal: Economic Theory

This paper is an attempt to expand the "classic" results on social learning that started with Bikhchandani et al (1992) and Banerjee (1992). Unlike the other papers in this field, Goeree et al (2006) allow for the following things:

• There are more than two possible states of the world, and agents have a nonnegative prior over all the possible states
• There are more than two possible actions that could be taken by agents
• The agents obtain a signal about the state of the world (by assumption the signals are informative, bounded, and not redundant at all)
• The signals and the prior allow the agent to have beliefs about which state of the world they are actually in
  • public beliefs
  • private beliefs
• The agents' payoffs have a private value component and a common value component
• The common value is fixed for all agents, and there is one for each unique (action,state) pair
• The private value component can be drawn from any distribution we specify
• But there is a joint density and (joint?) distribution of the private values by agents
• As a result, the agent's action can be completely driven by the private value component if the draw happens to be very large

I have some hang-ups about this paper from a casual reading in a rather uncomfortable cafe so maybe my impressions would change upon a re-reading.

1. The evolution private beliefs of the agents seem to be completely driven by the public beliefs of the agent
2. In this sense I do not understand why it is necessary to make a distinction between the private and public beliefs
3. The assertion is that "learning never ceases" in that the public beliefs between t and t+1 are never identical for any t
1. But even then this seems to be driven by the randomness of the private valuation realizations
2. Basically as long as someone makes a major mistake (in the sense that the public valuation completely overwhelms the common valuation), then "mistakes" allow people to "keep learning" about the true state
4. So basically it seems that the private vs. public belief distinction is unimportant - that the private valuation drives the results

Interesting things to look at later

• The martingale/submartingale discussion should be pretty cool to look at
• Is there a natural "stopping time" for these models? Even if learning never ceases, there should be some tolerance level where the difference between posterior beliefs of adjacent times becomes very small