Special Colloquium
Raghavan T.E.S.
UIC
Bob Aumann, the game theorist and the recent Nobel Laureate
Abstract: While von Neumann laid the foundations of game theory by proving the
decisive minimax theorem, his hopes to understand economic behavior via
cooperative TU games in characteristic function form, were never shared by
the so called neo-classical economists. Game theory in general and even
the works of Nash, remained outside the main stream of economic theorists
and their interests. By developing the general theory of cooperative
games without side payments and by proving the core equivalence theorem
for markets with a continuum of traders, Aumann was the first one to
overcome the shortcomings of TU games and show the power of cooperative
game theory to economists. Slowly economists were showing interest in
non-cooperative games and the problem of selling game theoretic ideas to
economists stayed with game theorists. Aumann and his galaxy of brilliant
students penetrated virtually every major center for economic research
with their new ideas in non-cooperative game theory like the theory of
repeated games, the theory of games with incomplete information, the
notions of correlated equilibria, Bayesian rationality, bounded
rationality, and so on. The subtleties of mutual knowledge and common
knowledge were clarified by Aumann and even in the case of some old ideas
floating in folklore, had to wait till Aumann laid the formal mathematical
foundations and made them precise. Often in models of bargaining or
auctions, players have to develop strategic manipulations in bargaining
or bidding with partial knowledge about the opponents. Text books after
1980 on game theory and microeconomic theory report in several chapters
contributions by Aumann and his school and their impact in understanding
economic models.
The talk will motivate some of his ideas via simple examples chosen from
literature. Even high school students should be able to appreciate the
ideas, though the formal proofs will challenge the best of mathematicians.
He invariably relegated the difficult proofs to the last sections of his
papers.
Friday December 2, 2005 at 3:00 PM in SEO 636