When: Friday, May 02, 3:30 p.m.

Where: 7500 (Special Location)Wean Hall

Vijay V. Vazirani, Georgia Institute of Technology

Aladdin Theory Seminar

Abstract:
In his seminal 1950 paper, John Nash defined the bargaining problem; the ensuing theory of bargaining lies today at the heart of game theory. In this work, we initiate an algorithmic study of Nash bargaining problems.

We consider a class of Nash bargaining problems whose solution can be stated as a convex program. For these problems, we show that there corresponds a market whose equilibrium allocations yield the solution to the convex program and hence the bargaining problem. For several of these markets, we give combinatorial, polynomial time algorithms, using the primal-dual paradigm.

Unlike the traditional Fisher market model, in which buyers spend a fixed amount of money, in these markets, each buyer declares a lower bound on the amount of utility she wishes to derive. The amount of money she actually spends is a specific function of this bound and the announced prices of goods.

Over the years, a fascinating theory has started forming around a convex program given by Eisenberg and Gale in 1959. Besides market equilibria, this theory touches on such disparate topics as TCP congestion control and efficient solvability of nonlinear programs by combinatorial means. Our work shows that the Nash bargaining problem fits harmoniously in this collage of ideas.

Dr. Vijay Vazirani is a leading researcher in algorithm design, and more generally, in the theory of computing. Throughout his research career, he as demonstrated a consistent ability to obtain novel algorithmic ideas, frequently of substantial mathematical depth, which while solving the problem at hand, also lay the groundwork for future contributions by others.

Dr. Vazirani's research career spans over twenty five years. During the first ten years, he made seminal contributions to the classical maximum matching problem which has historically played a central role in the development of the theory of algorithms. He discovered, jointly with other researchers, the fastest known sequential and parallel algorithms for his problem. Over the next ten years, Vazirani focused on approximation algorithms for NP-hard problems and had much influence on this area through work on several of its fundamental problems. In 2001, he published a book on this topic. He is currently working in algorithmic game theory, in particular on algorithms for computing market equilibria.

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