William F. Lucas, ORIE Professor for 15 Years, Dies at 77

William F. Lucas established a worldwide reputation as an expert in game theory, specializing in fair-division and voting systems.  After serving as a professor of operations research, mathematics and applied math at Cornell, he joined the faculty of the Claremont Graduate School, from which he retired.  He died in California June 7, 2010.
 

According to the Game Theory Society, of which he was a charter member, Lucas is best known for answering a question that had been open for more than two decades after the 1944 publication by John von Neumann and Oscar Morgenstern of Theory of Games and Economic Behavior, the seminal work in game theory.   The authors had proposed a solution concept (i.e. a means of allocating the total payoff) for cooperative games, i.e. those in which coalitions form among players and coordinated behavior can be enforced.   The concept is now called the N-M stable stet.  Lucas constructed a 10-player cooperative game meeting the criteria set down by von Neumann and Morgenstern but for which there is no N-M stable set, thereby answering the existence question in the negative. This led over time to the specification of alternative solution criteria. 

Prior to joining Cornell in 1969 Lucas was a mathematician at the RAND Corporation in Santa Monica, CA, which he later served as a consultant.  He was a graduate of the University of Detroit and the University of Michigan.  According colleagues, in addition to his research contributions he played a central role in shaping game theory and the game theory community while promoting the subject in the broader mathematics community through review articles, conferences, and workshops.  According to economics Nobel laureate Robert Aumann of Hebrew University, "Bill was great on what's nowadays called 'citizenship'"  in the academic world.

In June 2005 Lucas friends and colleagues John Maceli and Fred Roberts organized a "Lucasfest" at Claremont.  Maceli is Associate Professor of Mathematics at Ithaca College; Roberts is Professor of Mathematics at Rutgers.  Attendees arranged for a fund in his name at the Mathematical Association of America (MAA) to help supplement the cost of putting on summer short courses under MAA auspices.  One admirer commented that "Bill was a valuable gadfly for our mathematical community, calling our attention to new ideas and urging that they be introduced more quickly into the undergradaute curriculum."  Aumann, noting that Lucas promoted research on the N-M stable set, said "I still believe that it is the most subtle and beautiful solution notion in game theory, yielding many surprising and deep insights into a great variety of social processes."  

ORIE Professor Robert Bland recalls that Lucas was able to visualize objects in spaces of several more dimensions than three (his stable N-M counterexample has a representation in 10-dimensional space).  In order to help students visualize such objects, Lucas arranged to have chalk in a large variety of colors available in his classroom for use in portraying such examples on the 2-dimensional blackboard.

According to OR field member and Lucas colleague Professor Louis Billera, "during his Cornell years, Bill directed the dissertations of many students (more than one per year), several of whom have gone on to shape the field of game theory much as their advisor did in his time."  His Cornell students include:

• Richard Spinetto, Associate Professor of Operations Management emeritus, Leeds School of Business, University of Colorado Boulder.
• Ehud Kalai, James J. O'Connor Professor of Decision and Game Sciences, Kellogg School of Management, Northwestern University.
• Loren Cobb, Research Associate Professor of Mathematics and Sociology, University Colorado Denver.
• Peter Farquhar, Founder, Fox Strategy, LLC.
• Robert Weber,  Frederic E. Nemmers Distinguished Professor of Decision Sciences at the Kellogg School of Management, Northwestern University.
• Pradeep Dubey, Leading Professor of Economics, State University of New York Stony Brook.
• Prakash Pundalik Shenoy, Ronald G. Harper Distinguished Professor of Artificial Intelligence, School of Business, University of Kansas.
• Richard Engelbrecht-Wiggans, Professor of Business Administration, College of Business at Illinois.
• Shigeo Muto, Professor, Department of Social Engineering, Tokyo Institute of Technology.
• Mohamed Rabie
• Kai Michaelis
• David Housman, Professor of Mathematics, Goshen College, Indiana.
• Michael Hilliard, Center for Transportation Analysis, Oak Ridge National Laboratory.
• Andrew Sterge, President, Magentar Capital/A.J. Sterge Division, Philadelphia.
• Chih Chang, Professor of Mathematics, National Tsing Hua University, Taiwan.
• Johannes Heijmans, Assistant VP, Marketing Modeling and Data Mining, US Automobile Association.

In addition Lucas advised the dissertations of several students in other Cornell fields, including mathematics, applied mathematics and regional science.

In marking  his passing, John Maceli said that "There is an old cliche which starts with 'it doesn't matter' and ends with 'how you play the game.'  Bill Lucas 'played the game' with consummate ability and dedication and zest, and he has been a winner, not just for himself but for all of us."