Series: Mathematics Colloquium

Date: Thursday, November 21, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Leonid Vaserstein

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Kalyan Chatterjee, Economics, Penn State

Title: Some Mathematical Models in Business and Economics

Abstract:

The use of mathematical models in the analysis of problems in business
and economics has become widely prevalent in the last fifty years.
The earliest work, which still continues, has sought to build models
to give quantitative advice to decision makers in corporations and
falls under the rubric of operations research and management science,
with linear programming being the most widely-used tool.  However,
these techniques usually ignore uncertainty and competitive
interaction in markets, so their usefulness for strategic decisions is
often questioned, though they have been successful for operational
questions.  Game theory, which now plays an extremely important role
in economics, deals specifically with interdependence and competition
among decision-makers but is able to offer only contingent advice to
players.  Its primary use is to provide qualitative explanations
rather than quantitative advice.  This talk will focus on some themes
in the game theory literature.  One theme will begin from John Nash's
theory of bilateral bargaining (not Nash equilibrium) and its
relationship to modern bargaining theory, including extensions to
multiple players.  If time permits, I shall describe some work of my
own on learning and bounded rationality, and on the conditions under
which a contract with an award of permanent tenure is optimal.  (This
last falls in the literature on incomplete contracts.)  I shall also
try to fit in a fourth topic area, if there is time.  The aim will be
to give an overview of some directions of current research.