Tuesday, October 05, 2010

Economics meets computer science

I saw an interesting lecture by Vijay Vazirani on the cross-over between computer science and economics: The "Invisible Hand of the Market": Algorithmic Ratification and the Digital Economy. Starting with Adam Smith, he covered the development of algorithmic theories of markets and market equilibrium.

The first step was a proof that simple market models have equilibria. A very computational next question, then, is, "OK, these equilibria exist. How hard is it to find them?" Enter complexity theory.

Apparently, algorithmic game theory has been used to derive Equilibrium Pricing of Digital Goods via a New Market Model and was applied to cook up the pricing algorithm for Google's TV ads.

Attempts to compute equilibrium prices led Irving Fisher to develop his "Price Machine" in the early 1890's, which was essentially a hydraulic computer.

Vazirani wrote a book on approximation algorithms. I kept expecting him to introduce the idea that, while finding equilibria is very hard, markets approximate a solution. Maybe, given a set of conditions we could show that the approximation was within certain bounds of the true optimum. But, he didn't.

A few unanswered questions come to mind:

  • Can irrationality be modeled?
  • Do big differences in wealth or other asymmetries illustrate any divergence between the model and the real world?
  • Even if markets reach equilibrium in some theoretical long run, in the real world they're constantly buffeted by exogenous shocks, and therefore disequilibrium must be pretty common. He answered a question like this saying that no attempt to incorporate dynamics has been very successful.
  • Digital marketplaces like eBay or Google's Ad auction must provide a ridiculous treasure trove of data to be mined for empirical economics.

The Q&A session degenerated into politics pretty quickly. People asked about how the financial crisis might have challenged his models. One questioner asked about "animal spirits". Vazirani defended the neoclassical line and stated that their algorithms had "ratified the free market". The questioner responded that "The markets have ratified P.T. Barnum". Another audience member added "...because of government interference". It's surprising that people aren't able to differentiate between a theoretical result based on a carefully constructed model and political opinions in the real world, but that stuff belongs over here.