John Nash, the renowned mathematician and Nobel Prize winner in Economic Sciences, was greeted by a respectful and deferential audience when he entered the IBM amphitheatre on May 11. As the guest speaker for the 25th anniversary of the Group for Research in Decision Analysis (GERAD),* Professor Nash was at HEC Montréal for the 2005 Optimization Days, organized this year by GERAD. The event brought together some 400 researchers from around the world, from May 9 to 11.
New Methods for the Study of Co-operation in Games
Professor Nash, famous for his remarkable contributions to game theory, spoke on the subject of co-operative games between two or three players. In a co-operative game, players attempt to co-ordinate their strategies to optimize their joint well-being and determine a way of sharing collective wealth based on desirable criteria (equity, altruism, etc.). Professor Nash contrasted his sharing approach with the classic solutions in co-operative games.
An unusual life
In 1994, at age 66, John Nash shared the Nobel Prize for Economic Sciences with two co-winners. His work on game theory, including the Nash equilibrium and the Nash arbitration scheme, concepts that are applied universally today, has allowed researchers to better understand problems of competition and co-operation among agents (players) and to develop tools so as to come up with concrete solutions in a number of disciplines.**
In his 27-page thesis in mathematics at Princeton University, which he wrote at age 21, Nash proved his famous theorem stipulating the existence of a solution (Nash equilibrium) to all non-co-operative games. This finding had a phenomenal impact on economic analysis and applications in many other fields (including in political science, biology, ecology, etc.). John Nash’s unusual life was the subject of the famous book A Beautiful Mind, by Sylvia Nassar. The book was made into a movie directed by Ron Howard, and won four Oscars in 2002. Today, at age 77, the celebrated mathematician continues his research into game theory, at Princeton.
GERAD: 25 years of research and discoveries
John Nash’s presence at HEC Montréal was a wonderful way to mark GERAD’s 25th anniversary. The Group celebrated the milestone with an international symposium on May 12 and 13, following the Optimization Days. On May 11, it launched 10 commemorative books authored in part by HEC Montréal professors.
GERAD, directed since 2001 by Georges Zaccour, Full Professor with the Department of Marketing, is one of the five leading operational research centres in the world. The multidisciplinary centre brings together some forty professors and researchers, while over 180 MSc and PhD students collaborate on research projects. Since its founding in 1979, GERAD has developed expertise in a number of sectors, in particular transportation, energy and logistics. The numerous studies conducted at the interuniversity centre have led to real-life applications, including mathematical models and effective software solutions, many of them used around the world today.
Professors Georges Zaccour, from HEC Montréal, and John F. Nash, from Princeton University.
| * | GERAD is a joint HEC Montréal, École polytechnique, McGill University and Université du Québec à Montréal centre. |
| ** | Game theory deals with competitive or co-operative situations among interdependent economic, social, political and other players. |
