# Seminar: April 5

## Vijay Vazirani, Georgia Tech

## Extending General Equilibrium Theory to the Digital Economy

General Equilibrium Theory, the undisputed crown jewel of Mathematical Economics for over a century, gave a very satisfactory solution to the central problem of arriving at a principled method of pricing goods and services -- one that leads to an efficient allocation of scarce resources among alternative uses. The solution was based on Adam Smith's principle of maintaining parity between supply and demand, Walras' notion of equilibrium, and the Arrow-Debreu Theorem, which proved the existence of equilibrium in a very general model of the economy.

However, this solution, designed for conventional goods, is not applicable for digital goods -- once produced, a digital good can be reproduced at (essentially) zero cost, thus making its supply infinite. Considering the current size of the digital economy and its huge growth potential, it is imperative that we obtain an equally convincing theory for pricing of digital goods. In this talk, I will describe what appears to be a first step in this direction.

After taking into consideration idiosyncrasies of the digital realm, we give a market model that is appropriate for the digital setting, a notion of equilibrium for this model, and a proof of existence of equilibrium using Kakutani's fixed point theorem. For a special case, we also give a polynomial time algorithm and we show that a rational equilibrium always exists. Finally, I will outline a multitude of issues that still need to be addressed to obtain a theory for the digital economy that is on par with the original theory.

Based on the following joint paper with Kamal Jain: http://arxiv.org/abs/1007.4586