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It is not from the benevolence of the butcher, the brewer, or the
baker, that we expect our dinner, but from their regard for their own
interest. Each participant in a competitive economy is led by an invisible hand
to promote an end which was no part of his intention.
Adam Smith, 1776.
With his treatise, The Wealth of Nations, 1776, Adam Smith initiated the field of
economics, and his famous quote provided this field with its central guiding
principle. The pioneering work of Walras (1874) gave a mathematical formulation
for this statement, using his notion of market equilibrium, and opened up the
possibility of a formal ratification.
Mathematical ratification came with the celebrated Arrow-Debreu Theorem (1954),
which established existence of equilibrium in a very general model of the economy;
however, an efficient mechanism for finding an equilibrium has remained elusive.
The latter question can clearly benefit from the powerful tools
of modern complexity theory and algorithms, and was taken up in the earnest within
theoretical computer science a decade ago. In this talk, we will provide a summary
of key developments. We will also describe a fascinating new direction, for the
theory of algorithms, that has emerged from this work.
A compelling new issue is extending this deep understanding of markets to the
digital economy -- because of some fundamental reasons, the methodology outlined
above does not carry over to the digital realm. We will outline recent progress on
this issue.
Based in part on:
http://www.cc.gatech.edu/~vazirani/NBalg.pdf
and
http://arxiv.org/abs/1007.4586
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