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Game Theory and Operations Research University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange About Harlan D. Mills Science Alliance 1-2002 Game Theory and Operations Research Martin Shubik Follow this and additional works at: https://trace.tennessee.edu/utk_harlanabout Part of the Physical Sciences and Mathematics Commons Recommended Citation Shubik, Martin, "Game Theory and Operations Research" (2002). About Harlan D. Mills. https://trace.tennessee.edu/utk_harlanabout/11 This Article is brought to you for free and open access by the Science Alliance at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in About Harlan D. Mills by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. GAME THEORY AND OPERATIONS RESEARCH: SOME MUSINGS 50 YEARS LATER MARTIN SHUBIK Yale School of Management, 56 Hillhouse Avenue, P.O. Box 208281, New Haven, Connecticut 06520, [email protected] y its very nature, a discursive reminiscence has to be of game theory methods to operations research (Shubik Bsomewhat self-referential. Furthermore, it cannot offer 1953a, 1958a), economics (Shubik 1953b, 1953c), politi- an exhaustive survey of the many special topics to which cal science (Shubik 1954), management science (Shubik it may refer. Rather than suffer “strangulation by footnotes 1955), law (Shubik 1956), simulation (Shubik 1958a) and and references,” for brevity and equity I do not provide the decision sciences (Shubik 1958b). references to subjects such as auctions, the new industrial A basic problem that has beset the publication of organization, or experimental gaming because there are applications of operations research from its inception (in more than adequate references and survey articles available. both the United States and the United Kingdom) has been When I first skimmed The Theory of Games and Eco- the intermix between academic theorizing and practice. nomic Behavior in 1948, I did not really understand it, but I The introduction of the journal Mathematics of Operations sensed that this was the way to go in the study of multiper- Research provided a way to relieve Operations Research son conscious strategic behavior. I had heard a little about and Management Science of an overburden of the body of operational research casually in 1944 in two applications: mathematical theory developing to deal with specific sub- one concerning how to aim an anti-aircraft gun to take disciplines in operations research such as inventory theory, account of the plane’s motions during the time it took to linear, and integer programming. The creation of a special reach it after firing, and I had a vague idea that one could Practice Section in Operations Research in 1984 attempted try to analyze the best ways for convoy defense by using to make sure that there would be some segment of the jour- some form of mathematics. nal devoted to the “real world.” Michael Rothkopf (1994), The visit to the main library at the University of Toronto in a valuable survey article, discussed some of the reasons to look randomly at the new books in economics led to why practitioners may not write for the open literature. my going to Princeton to study game theory. To this day, Recently Omerod and Kiossis (1997) carried out a com- Ihave been struck with the thought that it is possible to parison of the nature of the publications in both United not know precisely what one is looking for, but recognize States and United Kingdom publications and concluded that immediately when one finds it. there were possibly even fewer publications of results in At Princeton, there was some direct talk about operations the United Kingdom than in the United States. research per se, and only a few of us were aware of the Because my main purpose is to cover the evolution of the newly formed Operations Research Society. But in a few relationship between game theory and operations research years around Fine Hall (and elsewhere), much of the math- rather than to review all of operations research, I limit my ematics relevant to its development was being developed. broader comments on operations research with a few Pan- Among the visitors, students, and faculty were Bellman, glossian remarks. It is my belief that operations research Feller, Gomory, Karlin, Kemeny, Kuhn, McCarthy, Mills, has been so successful that it may have put itself out of Minsky, Nash, Scarf, Shapley, Tucker, and Tukey. Dynamic business, at least in its easy-to-recognize sense. It has suc- programming, linear programming, convex programming, ceeded to the extent that it is taught in a more or less integer programming, inventory theory, game theory, arti- routine and watered-down manner in every business school. ficial intelligence, and applied probability were all being Linear programming, queuing studies, and elementary com- developed. petitive models go with the turf. While still at Princeton, and then when at the Institute for Consulting firms flourish. A variety of military opera- Advanced Study in the Behavioral Sciences and at General tions research firms make a good living off weapons anal- Electric in the period between 1953 and 1958, I was con- ysis; specialist firms such as Fair Isaac have found a vinced that the methods of game theory were going to have niche in credit evaluation; McKinsey dispenses general- a broad impact, not only on operations research but on the ized operations research and management science under behavioral sciences in general. I suggested the applicability avariety of names. RAND, Stanford Research Institute, Subject classification: Professional: comments on. Area of review: Anniversary Issue (Special). Operations Research © 2002 INFORMS 0030-364X/02/5001-0192 $05.00 Vol. 50, No. 1, January–February 2002, pp. 192–196 192 1526-5463 electronic ISSN Shubik / 193 Los Alamos, and many others may not be in their heyday— The third millennium has arrived; game theory proved its as they were when operations research was young and successes in many disciplines. The big gains were made. 100% improvement in performance almost anywhere was There is much in the way of valuable special results still to to be expected—but they still produce. Small groups of aca- be obtained. But much in the same way as one can regard demic consultants provide consulting services in the design the limited views and models of classical economics, and of auctions or in the structuring of games to study market the one-person conscious optimization problems that char- structure. acterized much of operations research as calling forth the Our “flagship journals” are academic journals, and the development of game theory, the limitations of game theory incentive structure for most practitioners to publish their have indicated that many of the big problems for which it findings in them is minimal. Validation in application is was designed need to be answered in a manner that can probably better measured by a repeat order from a cus- best be described as “post-game theory.” tomer than a publication in Operations Research. The goals The new game theory in operations research applications of academics in operations research and the goals of prac- lies in the study of organizations and in systems that involve titioners are basically different and can be appreciated only individuals, networks, and institutions. The success of game when placed in the context of the organizations for which theory in supplying the language for the study of informa- they work, their reward systems, and their life styles. tion and providing the basic concept of strategy has led to Iamreminded of one event that happened to me at our understanding the limitations implicit in the model of General Electric and another that happened to George the fully informed rational individual decision maker. The Feeney at Stanford Research Institute. I was complain- vistas opened up by the formalization of the concepts of ing to one of the vice-presidents that in spite of the fact player, information set, strategy space, and extensive form that General Electric in the 1950s had hired a first-class led us to gaming, simulation, and artificial intelligence. The group of operations researchers, the management, except stress will be on individuals with limited capacity, optimiz- for Harold Smiddy (Smiddy and Naum 1954 is still worth ing locally in many special contexts where expertise and rereading), did not appreciate us. Jack McKitterick replied learning count. that the trouble with the executives at General Electric was Economic man, operations research man, and the game that they had not understood the basic motivation of the theory player were all gross simplifications invented for group they had hired. He said if they had to do it over conceptual simplicity and computational convenience in again they would have paid us half as much but would have models loaded with implicit or explicit assumptions of sym- hired a special manager to stroke us and go around telling metry, continuity, and fungibility to allow us (especially in each of us how smart we were. George Feeney’s experience a precomputer world) to utilize the methods of calculus at Stanford Research involved explaining what operations and analysis. Reality was placed on its bed of Procrustes research was to one of their vice-presidents, who reacted to enable us to utilize the mathematical techniques availa- immediately. “I see,” he said, “operations research involves ble. Fortunately, there were many important problems in utilizing big minds to work on small problems.” Both of these observations may be regarded as flippant, but both military OR and mass economies that fitted comfortably contain just enough truth to be worth considering. Kirby into this picture. Cooperative game theory utilizes combi- (2000, p. 666), in a recent article, has noted that part of the natorics, but once one considers games with more than 5 crisis in OR from the 1970s to 1990s was that it had failed or 10 differentiated players, the calculations involving all to capitalize on its wartime strategic profile.
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