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On the Trail of a White Whale: Sequel Martin Shubik Simulation Gaming published online 18 April 2013 DOI: 10.1177/1046878113480456

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Autobiographical Article

Simulation & Gaming XX(X) 1–20 On the Trail © 2013 SAGE Publications Reprints and permissions: of a White Whale: Sequel sagepub.com/journalsPermissions.nav DOI: 10.1177/1046878113480456 sag.sagepub.com

Martin Shubik1

Abstract I offer a lengthy rationalization and an apologia pro vita sua for dreaming up, playing, experimenting with, and theorizing about games in various applications.

Keywords experimental, financial institutions, game theory, gaming, operational, teaching, theory of money

I must admit that I feel it is an indulgence to take time off to engage in this sort of puffery when one could be working or drinking a good Calvados, but a little self- indulgence can always be rationalized. I published an autobiography in 1997 titled On the Trail Of a White Whale: The Rationalizations of a Mathematical Institutional Economist (Shubik, 1997). Some 15 years later, this is an update. Frankly, I had not expected to last this long—but having done so and finding myself still on the trail, I continue with this scholar’s tale. In order to keep this essay self-contained and avoid asking the reader to return to the original source, here I give a brief summary of the 1997 text.

Early Trail Although some scholars have deemed it desirable to stick to a single narrow discipline and concentrate on strength in-depth, I have always been fascinated by problems that could not easily be categorized as pertaining to a single discipline. Thus, I have always been far more interested in political economy than in economics. The understanding of the role of money in a society calls clearly for an appreciation of law, politics, bureaucracy, and economics embedded in custom and history as well as rules

1Yale University, New Haven, CT, USA Corresponding Author: Martin Shubik, Yale University, Cowles Foundation, 30 Hillhouse Avenue, New Haven, CT 06511, USA. Email: [email protected]

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 2 Simulation & Gaming XX(X) and regulation. A single, narrow, analytical approach will not yield the depth of understanding of a topic calling for a synthetic approach. I noted before very different styles in scholarship. I belong to the small group of white whale hunters. This group consists of individuals who have selected an enormously difficult long-term project and stick with it until they finish it, or it finishes them. My task for over 40 years has been to attempt to build a decent abstract theory of money and financial institutions and to use the methods of game theory and experimental gaming to bolster the plausibility of such a theory. Shubik, age 2 Ever since my days as an undergraduate and as a graduate student, I have become more and more aware that analysis and synthesis should be regarded as complements rather than alternatives. I coined the term Mathematical Institutional Economics to stress the feature that this phrase is no oxymo- ron, but describes a bringing together of two allied approaches, static economic analysis and a context sensitive synthesis required to describe and understand socio-politico- economic dynamics. Context-free economic dynamics do not exist—the institutions of the society are its carriers of process. I have been fascinated with game theory since 1948, when I first encountered the great book of von Neumann and Morgenstern (1944). As a graduate student at Princeton, I learned that the language of game theory had provided a key to formaliz- ing the description of all forms of formal games and that these provided a first step in being able to start to develop a language for less formal games and for social processes. At that time, I did not know about rigid rule gaming, and the idea of free form gaming beyond the military had not yet been fully developed. At Princeton, along with the formal development of game theory, graduate students showed considerable interest in the playing of formal games such as CHESS and GO, and in inventing games that could illustrate different social or strategic phenomena. For example, a group of us invented a game called SO LONG SUCKER (see Shubik, 1954) where we wanted to design a game where, in order to win, you needed to form coalitions; but this was not sufficient for winning, at some point you needed to double-cross your partner. Thus, by 1952, in my mind, game theory and gaming were already linked. One stressed formal rules and analysis, while the other was concerned with describing actual institutions and with providing a way to investigate behavior. From Lloyd Shapley, I knew that gaming experiments had already been carried out at RAND, and when I was at the Center for Advanced Study in the Behavioral Sciences in 1955, I had heard about Merrill Flood’s and Anatol Rapoport’s interest in experimental gaming. During this time, I took a trip with Martin Beckmann to Yosemite, and one evening around a campfire, when Martin and I were discussing utility theory, an individual on the other side of the fire had evidently overheard part of our conversation and came around to join us. This gentleman was Sidney Siegel, an experimental psychologist

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and one of the earliest proponents of using experimental gaming in economics and psychology. We had an immediate rapport and in the next few weeks agreed on long- term collaboration when I returned to the East Coast. Sid was at PennState University and I became an adjunct research professor there, flying in around once a month from New York. Sid had committed himself to finishing a book with Larry Fouraker, but Shubik, age 15 we intended to work on a series of other experiments in economics, once he had finished his commitment. Our plans were cut short by his premature sudden death. After my year at the Institute for Advanced Study in the Behavioral Sciences, I decided to join the operations research group at General Electric (G. E.), which was very permissive in allowing time to maintain academic connections, hence my trips to PennState to work with Sidney Siegel were approved. I also met George Feeney at G. E. and we shared joint interests in the potentials of business gaming and simulation. In retrospect, we were naively optimistic on both counts. It took many years for the profession to evaluate the uses and limitations of business games. These games were, for the most part, rigid rule games with a fairly impoverished environment supplied. At the time, with the great advantages bestowed by youth, ignorance, and enormous optimism, we grossly underestimated the pitfalls and the poverty of our models. The computer was going to cure everything. People, organization, intangibles, and facts were ignored as minor problems. This also held for our early forays into simulation. We already understood that straight mathematical analysis could only take us so far. The power of the computer offered up the possibilities of building far better models and overall feedback systems of the various indus- tries in which G. E. had plants. We greatly underestimated the state of the art of simulation in the mid-1950s and the costs of data gathering and analysis. In 1960, I was on leave from G. E. to visit Yale. While there, with the aid of Jim Friedman, we built an analytical business game, this is, one in which we could actu- ally calculate much of the structure and generate fairly clean testable hypotheses. I decided to not return to G. E., but to accept an offer to join a research group at the T. J. Watson research labs of IBM, where I had the pleasure of colleagues such as Ralph Gomory, Richard Karp and Sam Winograd, Benoit Mandelbrot, and several others. Benoit and I became and remained good friends for 50 years, until his death in 2010. I built both an experimental game and a business training game (FAME) while at IBM for their Sands Point facility; but I was beginning to see the considerable gap between abstract theory together with rigid rule games and actual practice filled with imponderables that did not appear in the games. During my tenure at IBM, I spent a fair amount of time thinking about how to embed money into a general equilibrium setting in a natural and nontrivial way. I made no progress whatsoever beyond butchering several dozen unsuccessful models. Looking back after many years, I am reminded of a flip comment made by an eminent eye surgeon in reply to the question as to how one becomes an expert eye

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surgeon. He is reputed to have replied, in part seriously, in part in jest, “by butchering several dozen eyes.” Butchering several dozen mathematical models does not catch the imagination in the same way, but the message is the same. Learning and experience do not come cheap. Be grateful if one can learn at all. I have noted in Part 1 (1997) of this discourse, how while at RAND in 1970 while Young collegian looking at what I thought was a com- pletely different problem, the construction of a symmetric Cournot type game that was consistent with a general economic equilibrium structure. I finally was able to get the model right and discovered that this was the key to developing a formal viable theory of money. The extra commodity that I needed to build a viable model turned out to have an interpretation as money. Many years later, in discussions with Eric Smith, we observed that money behaves as does a catalyst in chemical processes. In economic mass markets, it enables trade to take place, while it remains unchanged by the trade. The getting it right for the strategic model was, for me a profound moment. It could, of course, have been a moment of profound self-delusion; but I figured at the time that that was a problem for the critics and not me. What I saw was that I had a viable process model of a closed economic system with full feedbacks. It meant that the tools were there to analyze this structure to examine the relationship between competitive prices and noncooperative equilibria, and also that it was now possible to build experimental game models of the whole economy. In the late 1970s, at a conference run by Vernon Smith, I gave a paper (Shubik, 1979) pointing out how the strategic market game formulation gave rise to the possibility for experimenting not merely with competitive markets, but with financial institutions. At that time, as I am often a fairly slow learner, I had failed to grasp that the strategic market game was calling for a new paradigm. It was not just about a real or abstract commodity called money, it was about control. My understanding of the importance of control was to come later. At this time, there was still an enormous amount of underbrush to be cleaned up.

The Scholar’s Tale Continued Prior to starting my new tale, I must warn the unsuspecting reader that several quite different threads are woven together and that what might be crystal clear to those with one background may be as murky as mud to others. Thus, although I try to combine my interests in the theory of money, game theory, and experimental, operational, and teaching gaming, together the full blend may be hard to grasp. My recommendation is to let the eyes glaze over as one skips any technical commentary on material not in one’s discipline.

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Unfortunately, although in some quarters it may not be recognized, an understanding of the role of money in society calls for a difficult mix and blend of analytical and institutional understanding. It calls for a delicate appreciation of context. Those who understand operational gaming fully appreciate the various gradients between rigid rule games (like CHESS or the first business games) and the political military exercise. In my time spent at RAND as a consultant, I was deeply impressed and appreciative of the subtlety that a military historian such as Harvey DeWeerd could attach to the formulation of a game. The more I began to understand some of the problems in investment banking, the more I began to appreciate the blend of the quantitative and the qualitative in the way the monetary system works. The years from 1970 to 1999 were years of plodding through small problem after small problem. My attitude was that I had an overall vision of what a theory of money was going to look like, but so many facets existed that I had to separate different small aspects of the overall picture that were amenable to analysis and in- depth study. A reasonably apt analogy is that of In the navy trying to assemble a large and fairly abstract jig- saw problem. One may have an overall insight as to what the major overriding pattern looks like, but as local detail is cleaned up, the vision becomes clearer and the understanding of the whole becomes deeper. I will not bore the reader or myself with the details on the slugging through of the many bits and pieces assembled in the understanding of basic simple process models provided by the structure of strategic market games. For those who might be interested in detail, somewhere in my publication list between Item 69 and Item 262 of a list that is far too long, one can pick out the important items. I comment on the fact that my publication list is far too long not as a matter of a false sense of modesty, but because at this stage of my career, I can afford the joys of a high level of honesty without the niceties of having to pander to any particular group or club as to whether I am doing the right thing or not. The honest list of publications of virtu- ally any economist, or for that matter any physical scientist alive or dead, contains well under 20 publications with few if any exceptions. In spite of the current craze to pro- duce a welter of rank orderings of the authors in any profession, the better sorting device is probably 200 years of social and professional digestion after which the three or four hundred article publication list either disappears or emerges slimmed down to a handful. I make no attempt to select for an audience of other than myself what I believe to be my 10 most important publications. By the measures of the number of times quoted,

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 6 Simulation & Gaming XX(X) my brief piece on THE DOLLAR AUCTION GAME (Shubik, 1971) might be regarded as one of my important publications; but white whale hunters are not concerned in any detail as to whether an incidental catch of a mackerel or two is appreci- ated or not. My years from 1970 up until 1999 were primarily involved in assembling the material for my two volumes, The Theory of Money and Financial Institutions, Volumes 1 and 2 (Shubik, 1999a, 1999b). They are not merely my work, but are also in part the work of many colleagues who were willing to risk the dangers of working with someone vaguely tolerated by, but not in, the economic establishment. The individuals include John Mayberry, John Nash, Lloyd Shapley, Sidney Siegel, Gerald Thompson, Jim Griesmer, Gerrit Wolf, Tom Quint, Matthew Sobel, Martin Whitman, Ward Whitt, Pradeep Dubey, Charles Wilson, John Geanakoplos, Shuntian Yao, Siddharta Sahi, Jingan Zhao, Andreu Mas- Colell, Rabah Amir, William Sudderth, Ioannis Karatzas, John Miller, Dimitri Tsomocos, Michael Powers, Imelda Yeung, Per Bak, Maya Paczuski, Eric Smith, and Kai Nagel. I do not feel that these two volumes cleaned up all of the detailed problems that still merit About 1958 investigation without even going near to the control problem that my work was leading me toward. However, the roles of different market structures, the importance of bankruptcy and default laws, and the distinctions among perishable and storable consumable goods and capital goods yielding streams of services were clarified. While the work noted above was in progress, I continued my labors on gaming, I taught several courses on gaming and published four books on gaming, Games for Society, Business and War (Shubik, 1975a); The Uses and Methods of Gaming, (Shubik, 1975b); The War Game (Brewer and Shubik, 1979); and Market Structure and Behavior (Shubik & Levitan, 1980). The first book noted above was highly dis- cursive, and argued that, for the social sciences, business, and the military, games for teaching, training, and experimentation were a natural set of tools. The second book was essentially a service to the profession. No decent compen- dium and classification of the literature was easily available at that time, hence in part to satisfy my curiosity and to provide some encouragement for others to study gaming, I put this collection together. The third book was done jointly with a former student and currently distinguished colleague who has since specialized in ecological problems. At that time, we were both deeply interested in war gaming. It is easy to forget that the very basics of gaming for training and for operational purposes were provided by the military. To ignore and fail to capitalize on an extant body of knowledge because it happens to come from the

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army or the church or some other tainted source has always seemed to me to be folly. We had the opportunity to do a coun- trywide survey of all of the military games and simulations in the USA, and we regarded it as both a source of scientific interest and a way to understand the inter- faces among science, bureaucracy, and politics. The fourth book noted was essentially The Shubik family a companion volume containing the theory behind the business game I had constructed at Yale. It was badly laced with typos, which highly limited its usefulness; mea culpa. When I look back at these labors and the evolution of my thoughts about gaming and simulation over the years, one item that came to mind concerns my reactions to a great book by Hesse (1968) titled The Glass Bead Game (German: Das Glasperlenspiel). The interpretation of the Glass Bead Game that suits my purposes is the ever-present fight between bloodless abstraction leading to higher and higher levels of elegance and intellect combined with a progressive sterility that disconnects the authors from their environment. In contrast with the abstract game players, a Dominican scholar, Father Jacobus whose character is based on the historian Jakob Burckhard, poses a humanitar- ian challenge to the master of the game. Going from the sublime of great literature to the more mundane concern with gaming and the social sciences, the warning is there. It is easy in the social sciences in general and economics in particular to allow the mathematical abstraction to reach the point where the disconnect from context poses a dan- ger to the purpose and worth of the scholarship. Institutions are the carriers of process and cannot be abstracted away. It is possible that Hesse’s own interpretation was far from mine, but in social systems, the meaning of the message sent and its interpretation by the recipient may differ. In the 1990s, I became a member of the external faculty of the Santa Fe Institute and this had a profound effect on my thinking. In many ways, it reminded me of the excitement and passion I had felt at The Center for Advanced Studies in the Behavioral Sciences in 1955 and RAND in the 1960s. I was to find 40 years later that I could still be associated with an establishment where ideas from different disciplines still bub- bled over and intermixed. I have always been gun-shy of interdisciplinary love fests where individuals who claim to be interested in everything get together to build a brave new world, or science, or playpen. I find that it is important in institutes devoted to interdisciplinary endeav- ors that the price of admission for each individual should be a clear expertise in some discipline and a willingness to listen to others. Quasipolitical enterprises such as The Club of Rome are replete with silver tongues and simplistic solutions that have public appeal. They pose a deep challenge to the scholar with a social conscience. The layman sees the institutions with the veneer of

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 8 Simulation & Gaming XX(X) science far more appealing to present needs than the think tanks worried about basic knowledge, even though they are relevant to fundamental problems concerning human existence. By the year 2000, I had begun to appreciate that I needed to write a third volume on the theory of money that differed considerably from the first two, in the sense that it was far more institutionally oriented. In a response to some constructive, though casual, critical remarks by Ken Arrow that as soon as one tried to introduce institutions into general equilibrium analysis, one was going to be deluged with an astronomical number of special cases, I hit upon the idea of minimal institutions or mechanisms where About 1967 the minimality was established in terms of the smallest strategy sets each individual required in order that a game could perform a specific function such as price formation, or life insurance, or control of the money supply. This was clearly an exercise in tracking down micro-micro-variables, but it can be done and I argued in my first two volumes that there were only three minimal mechanisms needed to form price (where the differences among them were slightly different requirements concerning strategic freedom; see Shubik, 1999a, Chapter 5). One of my goals for Volume 3 was to consider stock markets, insurance markets, and banks and central banks, being painfully aware that I could only try to get a minimal mathematical model for a single function for each of these multifunctional institutions. At the least, I could also provide a verbal historical description of their development. It was in beginning to lay out this program that it occurred to me that the basic item that had been staring me in the face for several years was that the extra degree of freedom imposed by introducing paper money had provided the underpin- nings for the governmental control problem of managing the money supply. The strategic market game structure could be reinterpreted as providing a new paradigm for the extension of the general equilibrium analysis to a formal game with one atomic or really large player, anywhere from 10%-50% of the economy and a set of small agents. Since 1970, with several probability theorist colleagues, I have been working on dynamic programming models of the economy. I had originally planned to do joint work with Richard Bellman, to whom, as an old friend I suggested the possibility of using his dynamic programming methods in application to dynamic microeconomic models of the economy. Our plans were shattered by his acquisition of a brain tumor. I had the good fortune to obtain the collaboration of Ward Whitt (Shubik & Whitt, 1973) and then loannis Karatzas and Bill Sudderth (see, for example, Karatzas, Shubik, & Sudderth, 1994) At that time and to this day, I thought that the low-dimensional (in cross-section) problems were of little direct use in applied micro- or macroeconomics as they were so painfully low dimensional. The macroeconomic work on rational expectations received considerable accolades in spite of my pessimistic view that

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these relatively toy models could not serve for sound macroeconomic policy advice, but could serve to provide experimental games to see if at least in a highly simplified experimental context rational expectations are borne out. We have not run such an experiment, but it is my hope and intent to be able to do so before my borrowed time runs out. You will find technical details concerning the difference between representative agent and individual agent models. In essence, both from the point of view of theory and the representation of the societies that we live in, I believe that many important ques- tions that cannot be answered without taking into account the wealth distribution within a society and the representative agent models fail to do this. It is probably reasonable to guess that further work utilizing fully dynamic models must proceed in the direction of calcu- lation, gaming, and simulation of special cases; but this is what applied macroeconomists and war gamers have been doing for some time when ad hoc problems such as specific economic or military problems are being considered. At the Santa Fe Institute, I started in on two long-term collaborations, one with Per Bak and a fruitful collaboration with Eric Smith, who though holding a PhD in physics, has consider- About 1977 able expertise and interest in physics, biology, linguistics, and economics. I deal first, briefly with my work with Per Bak and colleagues. I was sensitized to the possibilities that the newly forming subject of econo-physics might hold promise for basic economics as contrasted with its overwhelming concern with the stock market and finance. I have always welcomed the new, but at the same time I have been cautious about fads and loose analogies. Generations of economists have wasted time on the ill-defined physics-like classical PQ = MV equation in economic theory, first suggested by the Yale physicist Simon Newcomb. The problems lie in the microeconomic dynamics inade- quately described in a casual aggregation of poorly defined quantities. Per and his wife Maya Paczuski and I (Bak, Paczuski, & Shubik, 1997) produced a physical model of random trade encounters in a stock market, which was very much in the spirit of an application of econo-physics to finance. We followed this article with another one more to my interest on the dynamics of money (Bak, Nørrelykke, & Shubik, 1999), which may be regarded as related both to the work of Jevons and the failure of the double coincidence of wants and to the work of Kiyotaki and Wright (1989). In our article, the dynamics required for the support of equilibrium with money was explored. I sometimes feel like Typhoid Mary, my collaboration with Per was cut off by his untimely death, thus stretching my record of deadly collaborations to three.

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My discussions with Eric Smith, coming as they did while I was trying to sketch out an understanding of what a politico-economic theory of money had to encompass, has led to a collaboration that still lasts today. We were fascinated with the role that symmetry plays in economics and collaborated in generalizing Jevons’ famous paradox of the failure of the double coincidence of wants (Shubik & Smith, 2005). The paradox Kitchen games, about 1983 is used to show that one could construct an economic model with three goods and three individuals, whose roles were intrinsically symmetric in a way such that if they traded for direct gain only, in pairs there would be no trade, but if exchange prices were posted they would trade happily. This example plays an important role in understanding the role of money and markets in exchange. In our work, we became progressively more and more convinced about the importance of considering models in political economy, where more than one process was going on and that these processes took place on different time scales. This led us to compare two different economies, one with gold as money, with the supply in control of the mining industry, and the other, an economy with fiat money, with the expenses of a central bank, bureaucracy, legal establishment, and justice system to be paid for by a government in control of taxes and the money supply (Smith & Shubik, 2011).1

Personal Life In this discourse, I have purposely avoided references to my personal life as much as possible because they are of primary concern to family and friends and few others. The basic data are on my website, and as is often the case with a reasonably pleasant existence, they are fundamentally unexciting. I believe in the curse “May you live in inter- esting times,” even though its provenance appears to be dubious. I part from silence on personal matters here because the unfortunate events in the first couple of years of the new millennium influenced my working style quite heavily. I had three medical problems in short sequence such that since then I have the constant feeling that I am living on borrowed or stolen time and that I have to work faster. In a fairly swift sequence, I had the joys of a lymphoma, the cancer was swiftly followed by a massive pulmonary embolism, and then somewhat later I was diagnosed for a rare and currently incurable autoimmune system disease known as Inclusion Body Myositis (IBM!!) that slowly, but surely destroys the muscles in the legs and arms. At least, the first two maladies gave me a break to read all of Boswell’s Life of Johnson and the volumes by Macaulay on The History of England. An amazing amount about financial institutions exists as well as the role of bureaucracy, in the latter. My third disease has had stranger influence. As it is slow and without known cure, apart from trying to contribute resources to help to find a cure the only choice is to

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 Shubik 11 adjust as best as one can. As the pleasant distractions of the active physical life become more and more difficult and eventually drop off one by one, be they hiking, canoeing, travelling, or visiting museums, more time is freed up for more sedentary alternative occupations and to a white whale hunter the alternative is simple. The impact of the onslaught of disease forced me to reorganize my thoughts as to how to proceed. The vision was getting clearer on the functioning of money and financial institutions as a perception, evaluation, and control system with a dominant control agent dependent on information and evaluation from others. The rug merchant, about 1990 I started to see more and more that, although much of economics is analytical and biased toward relatively short-term conscious behavior, the system as a whole is clearly evolutionary, with no inconsistency in having an evolutionary system driven in part by local optimizers. Serious illness combined with age serves to remind those of us with a heavy agenda that little time is left and that one had better reorganize under the assumption that one is never going to finish, but that does not much matter. What matters is to stay on course, do what one can do, and try to make clear to others why it is worth doing.

Pursuing the White Whale When I first launched into tackling a theory of money and financial institutions, I was looking for a way to extend general equilibrium toward a reasonably well-defined dynamics. I did not see how it calls for a complete grafting of a control and perception system onto the whole economic body. I also did not foresee that connections to both physics and evolution would emerge more or less as logical necessities. Minimal institutions can be defined, but they are differentiated components of a more complex organism contributing to and requiring a high degree of coordination. What looked like a straightforward problem in mathematical economics and game theory involved the opening up of an elegant economic structure to dynamics. Although it was easy to be seduced by mathematical toys, a far more profound change in paradigm than I had bargained for had to take place. Money connects the timeless preinsti- tutional forms of general equilibrium and the price system to the polity and society. The attractive myths of the competitive price system supported by an equilibrium analysis that has great appeal to the naïve disappear when one tries to construct a process model with even the most minimal of institutions. The financial institutions emerge as carriers of process, centers for evaluation, and financial power reflected by the rules of the game. However, in a society, the rules are not static; they change under social pressures reflected through the political control system on the economy. The financial systems and monetary flows transmit the pressures between the polity and

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 12 Simulation & Gaming XX(X) the economy in both directions. The roles of both physics and evolution emerge in the nature of the dynamics. After my change in health, I changed my plans and the nature of my collaborations in order to work on and interweave four basic themes, simultaneously aiming at trying to complete four in-depth technical books with colleagues and one more descriptive and integrative volume where the assertions, conjectures, and observations on behavior and structure together would be linked with the more in-depth work, the overlying themes being politico-economic theory, institutions, and experimental games. I have continued, full speed ahead on all fronts. At the start of 2011, Volume 3 of the Theory of Money and Financial Institutions appeared. It has embryonic chapters on minimal institutions, including markets, banks, stock markets, insurance companies, clearing houses, and central banks. The direct help or wisdom of Michael Powers (Powers, Shubik, & Yao, 1998), Dimitri Tsomocos, Charles Goodhart, Pradeep Dubey, Siddharta Sahi and many others is gratefully acknowledged. This volume laid out, but did not go into much formal modeling or mathematical detail about the basic control and coordination problem that was emerging. However, already some clarity was beginning to emerge as to just how badly static competitive theory both in economics and finance papers over items such as corporate goals and control, the payment of dividends, the goals of the central bank, and the role of bureaucracies of large firms organized labor and government as well as the meaning of reserves and liquidity. At home, about 1997 The next item on my list has been a book with a colleague in mathematics and operations research (Quint & Shubik, 2013) that we have recently completed. It examines the control problem and goals of highly simplified, but fully mathematically formulated models of money-lenders, banks, and central banks under different conditions of monetary and credit constraint. We half- seriously, half-jokingly refer to it as “death by Lagrangian Multipliers” as unsurpris- ingly the understanding of control calls for an understanding of inequalities. These inequalities measure the pressure on the constraints in the allocation of investments, and from a more psychological point of view, indicate how the financial institutions serve as the perceptors or viewing devices of an economy measuring pressures before allocating money and credit. A dynamic economy seems to be almost always operating on some boundary regions and the strength of the pressure from the inequalities is critical. The crawling through model after model distinguishing many monetary and credit arrangements was simultaneously boring and enlightening in coming to grips with the understanding of the roles of perception and power of financial institutions. I have already noted some of the work with my colleagues loannis Karatzas and William Sudderth. We have concentrated on a variety of low-dimensional parallel dynamic programming microeconomic models of the economy and some of these models have been used by my colleagues Juergen Huber and Shyam Sunder for experimental microeconomics.

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A goal only partially achieved at this time (Shubik & Sudderth, 2011) is to achieve an appropriate dynamic programming model of cost innovation reflecting a Schumpeterian approach to competition via innovation. It is my guess that, although Schumpeter’s (1911/1934) great work on the role and financing of innovation in a competitive economy justly deserves its fame, many of his insights might have come from his classmate, Felix Somary (1986), who became a highly practical and insight- ful Viennese banker. Although it has now been a 100 years since Schumpeter wrote, satisfactory formal mathematical models of innovation have been difficult to construct. Our goal is to consider both a mathematical analysis and an experimental game. The first is to take a simple model of an important form of innovation (cost innovation) and to show how, by the addition of successive, but highly relevant, features the original model that yields to an equilibrium analysis can no longer be handled usefully without considering path- dependent outcomes as suggested in the work of Brian Arthur (1994) on increasing returns. The second stage is to use the mathematical models for an experimental game. A complementary but different approach to economic analysis has been adopted in my ongoing work with Eric Smith at the Santa Fe Institute. Our attitude is and has been that the basic approaches and techniques in Physics have much to teach economics. In particular items such as what are our assumptions concerning the treatment of the role of time, symmetry properties, dimensional analysis, scaling properties, and the selection of grid size. These techniques, well known to physicists appear to have considerable use in economic modeling. We used these techniques in constructing and contrasting two strategic game models of the economy already noted above with gold as the money and with a paper money whose issue is controlled and usage enforced by a government bureaucracy. Eric and I have been working on a small book devoted to the applications of these methods to economics. Although, as yet, I have not been able to construct a satisfactory experimental game with a bureaucracy, I believe that in the actual providing of economic advice to any specific economy, the understanding of bureaucracy and the time lags and limitations it places on any program is a must. I believe that the economic guid- ance of any nation could be improved considerably by the construction of a gaming facility such as that at the U.S. Naval War College. A large Political Economic exercise, partially rigid rule (with macro- and microeconomic models) and heavily free form should be played to test major policy and tax proposals. Although I have advocated such a game for many About 2002 years, I believe that the bureaucratic and political forces against such a construction have to be large because such a game would be able to patch up ahead of time many of the loopholes in the proposals that take care of the friends or constituents of the sponsors of the proposals. The unifying force of national security that is present in the major war games would not be present in the

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politico-economic games even though experi- enced operational gamers might expect them to succeed. I have been fortunate in the past few years to have had the collaboration of two colleagues, Shyam Sunder at Yale and Juergen Huber at Innsbruck in the carrying out of a series of gaming experiments in order to test various hypotheses deriving from basic economic theory concerning the functioning of markets and financial institutions. I mention only three of our experiments. We have tested the efficiency of three mini- Recent mal market institutions for deriving competitive price (Huber, Shubik, & Sunder, 2010b) also comparing the behavior of the experimental participants with extremely simple artificial agents. We did this in order to consider the proposition that the appropriate design of a market institution may even enable the relatively unintelligent to do reasonably well on the average. We then built a game to examine an item of enterprise mythology concerning the possibility that every individual could efficiently issue his or her own credit, thereby dispensing with both the need for either gold or fiat as money. The economy would be a pure credit economy with no monetary substance, real or imaginary. Fisher Black (1970) wrote an article on this possibility; Sahi and Yao (1989) and later Sorin (1996) produced models of strategic market games having the conditions necessary for such a possibility. We built and ran an experimental game based on these models and were able to establish that indeed a game could be constructed that would have all individuals issue their own currencies successfully and achieve economic efficiency; but as is often the case, the devil is in the detail. Experimentally feasible, but institutionally improbable utopian, conditions are required for the perfect credit economy to work. In a perfect world with free communication, complete information, costless accounting, and a perfectly policed, costless clearinghouse, we built the utopian system (Huber, Shubik, & Sunder, 2010a) and verified the theory. The computerized networks of foreign exchange are about as close an approximation as one can get. With around 200 countries and 7 billion individuals in the world, what may work for high information and reputation conditions on 200 does not easily go through to 7 billion. We ran an experiment on the financing of the maintenance of a public good, considering first an omniscient government that can calculate and enforce an optimal tax rate in the economy, second an economy with a group of voters who vote to fix the tax rate every four periods, and then a game with individuals who support the public good with voluntary contributions. Our results have been pleasantly unsurprising. The ideal government is unreasonable from the point of view of information and bureaucracy problems in reality. A voting institution contrasted with leaving matters for voluntary contributions does fairly well.

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We expect that within the next year, we will test a model with innovation and then consider the underly- ing reality of rational expectation models with uncertainty. My overall expectations and conjectures are as follows. You will not find a fundamental dichotomy between behavioral and optimizing economic models. They lie on a continuum depending on the context and the complexity and frequency of decision making. In particular, the presence of exogenous uncertainty qualitatively degrades performance of individuals other than those highly trained in risk analysis in highly specialized contexts. Furthermore, in actuality, the problem is compounded by the distinctions between quantitative measures of risk and qualitative understanding of risk. In our experiments, Book cover we intend to look only at the simplest problems, but I conjecture that even there, the handling of risk by untrained individuals is highly limited.

Prisoner’s Dilemma All of the work above pertains to labors on the theory of money and financial institutions. I want to note briefly a few other items pertaining to game theory and gaming. In particular, the well-known PRISONER’S DILEMMA game when considered as a strictly ordinal 2 × 2 bimatrix game has 575 other companions. These 576 games can be regarded as the complete set of all alternative strategic structures, where each individual has only two strategic choices. Fortunately, by considerations of symmetry, they can be reduced to 144 games. Much is known about the PRISONER’S DILEMMA and several other special matrix games, but little is known about how players would play many of these games. One of the reasons for this state of affairs is that mass experimental gaming is costly and time-consuming. It is my belief that this difficulty can be somewhat over- come by presenting games on the web and offering modest prizes to a mass of players. I have had such a gaming platform built and have run it with some success with more than 50 participating players. The platform is available to anyone who is interested in using it. We are still in the process of considering how to expand its uses both as a teaching and experimental Book cover device. An essential part of my approach is that large statistics obtained cheaply with less controls than one might like in a dedicated laboratory are worth obtaining. I

Downloaded from sag.sagepub.com by DAVID CROOKALL on August 1, 2013 16 Simulation & Gaming XX(X) conjecture that the frequency results for the games with mixed strategy equilibria will not be significantly close to the predicted probabilities. In the development of the social sciences, the gathering of mass statistics of individuals behaving in formal games appears to me to offer a valuable source of data. For years I have wondered, without success, about how to turn the activities at Las Vega into valuable data. Could one design some formal experimental nonconstant sum games that would be played for a small admission fee and provide a self-financing source of data? I have discussed primarily games for research in theory and experimentation. In the last few years, my priorities have been such that I have been involved less in operational gaming and teaching. However, it is my belief that the explosion in games for entertainment and the general development of computer and communication techniques will serve as platforms for both new teaching and operational games. This relatively brief autobiographical sketch is obviously loaded with the word “I” and many self-references. It would be false modesty for any individual writing an autobiographical piece to have it otherwise. Yet at the same time, even if one views oneself as a fairly solitary traveler, far from the accepted wisdom of the establishment, intellectual honesty and courtesy requires that one appreciate and understand the contributions of others, even though one may differ profoundly with their approaches. No matter how far one wishes to paddle from the mainstream, the flow of new books, journals, and talks must at least be checked. It does not matter if you do not know the mathematics or understand the details of the statistical tests; the idea, the conclusions, and the earmarks of the talent of the authors are what count. One does not have to be a peer of the highly talented in any field to be able to assess talent and quality in most fields. It is especially rewarding to spot the potential for great talent in the young. That is what intellectual investment banking is about. Technique is to be admired and valued. Serious tool-making cannot be underestimated; but technique and tools without soul and insight can lead to sterility. My overall synthetic view has been as a solitary researcher, but much of the building has been with colleagues far more talented than I am in special fields. I regularly talk with Adam Smith, Hume, Ricardo, Keynes, Marshall, Cournot, Edgeworth, Jevons, Macaulay, Morgenstern, Simmel, von Mises, Schumpeter, Sun Tsu, and some others. They are dead in body, but not in intellect. In my three volumes on the theory of money, I have noted a considerable number of micro- and macroeconomists whose works have instructed me, yet my ability to communicate with most of them has remained minimal. Among the living economists, I may have been able to persuade a few, but I am almost mystified as to why several points that I have been trying to make that to me are almost trivially obvious points in the development of a scientific discipline are regarded as irrelevant or unimportant to economic science. It is my belief that much of serious science lies in the clean explanation of items that the practitioners, anxious to be of “real use in the real world” regard as minor annoyances or trivial inconveniences that need not be dealt with by those who want to deal with real processes.

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In the development of the understanding of a control theory of money, the features still to be explained include the role and the meaning of default and bankruptcy, as well as the meaning of liquidity and the understanding of what are a central bank’s reserves. Many other items remain and this is not meant to be primarily a lecture in the theory of money. It suffices to say that money turns out to be a major systemic property of a dynamic organically changing economy. From one point of view, it is a substitute for trust; from another point of view, it is a perfect catalyst. The financial institutions provide the neural network and the perceptions of the economy. Together, they enable the production and distribution of goods and services, the life blood of the economy, to take place. This is a far cry from the numeraire, the means of payment, and the store of value of the textbooks. They are all there, but their meaning is transformed and many other functions involving information, communication, and control have joined them. Much remains to be done. I do not have the luxury of the time to look backwards more than this essay has called for. To some extent, I and a few of my acquaintances and friends have had the luxury to be able to be autodidacts. Being able to teach oneself as well as to learn from others is a possibly selfish luxury. A necessary, but not a sufficient, condition for advance in understanding is to be able to be unfet- tered by the establishment; but it is one matter to ignore the existing body of knowledge and another to recognize it and to go in a different direction. It is time to go back to work.

Appendix: Bibliographies of Work by the Author, by Category Gaming A. Books Games for Society, Business and War. (1975). Amsterdam, Netherlands: Elsevier. The Uses and Methods of Gaming. (1975). New York, NY: Elsevier. The War Game (with G. Brewer). (1979). Cambridge, MA: Harvard University Press. Political Economy, Oligopoly and Experimental Games: The Selected Essays of Martin Shubik Volume One. (1999). Cheltenham, UK; Northampton, MA: Edward Elgar Publishing Limited.

B. Articles 1960-1961 Simulation of the industry and the firm. (1960). American Economic Review, 50(5), 908-919. Comments upon games as a teaching device. (1961). In Proceedings of the Conference on Business Games (W. T. Dill, J. R. Jackson, and J. W. Sweeney, Eds., pp. 134- 135). New Orleans, LA: Tulane University.

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1962-1963 Some experimental non zero sum games with lack of information about the rules. (1962). Management Science, 8(2), 215-234. Oligopoly bargaining: the quantity adjuster models (with L. E. Fouraker & S. Siegel), partially reported in Siegel and Siegel, Bargaining Behavior. Hightstown, NJ: McGraw-Hill, 1963.

1964-1965 Experimental gaming and some aspects of competitive behavior. New Perspectives in Organization Research (W. W. Cooper, H. J. Leavitt, & M. W. Shelly, Eds., pp. 449-463). New York, NY: Wiley, 1964.

1966-1967 Some Comments on Gaming for Teaching and Research Purposes. (1966). In Simulation Models and Gaming. White Plains, NY: IBM Data Processing Division.

Game Theory, Operations Research, and Theory of Money A. Books Readings in Game Theory and Political Behavior. (1954). New York, NY: Doubleday. Strategy and Market Structure. (1959). New York, NY: Wiley. [Spanish Edition— Estrategia y Estructura de Mercado, Barcelona: Omega, 1962. French Edition— Strategie et Structure de Marches, Paris: Dunod, 1964.] Game Theory and Related Approaches to Social Behavior. (1964). New York, NY: Wiley. [German Edition—Spieltheorie und Sozialwissen-schaften, New York: Wiley, 1964. Japanese Edition—New York: Wiley, 1969.] Essays in Mathematical Economics in Honor of Oskar Morgenstern (M. Shubik, Ed.), Princeton, NJ: Princeton University Press, 1967.

B. Articles 1952-1953 A business cycle model with organized labor considered. (1952). Econometrica, 20(2), 284-294. Information theories of competition and the theory of games. (1952). Journal of Political Economy, 60, 145-150. [Also translated into German as “Information, Wettbewerbs theorien und die Spieltheorie” in Hans-Heinrich Barnikel, Wettbewerb und Monopol, Wissenschaftliche Bucghesellschaft, Darmstadt, 1968.] A comparison of treatments of a Duopoly situation (with J. P. Mayberry and J. F. Nash). (1953). Econometrica, 21, 141-154. Non-cooperative games and economic theory. (1953). In Report of Conference on the Theory of N-Person Games, 20-23. Solutions of N-person games with ordinal utilities (with L. S. Shapley). (1953). Econometrica, 21, 348-349.

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Game theory and operations research. (1953). Journal of the Research Society of America, 1, 152. The role of game theory in economics. (1953). Kyklos, 7(2), 21-34.

1954-1955 A method for evaluating the distribution of power in a committee system (with L. S. Shapley). (1954). American Political Science Review, 48(3), 787-792. Introduction to the nature of game theory. (1954). In Readings in Game Theory and Political Behavior, (M. Shubik, Ed.). New York, NY: Doubleday, 1-11.

Declaration of Conflicting Interests The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author received no financial support for the research, authorship, and/or publication of this article.

Notes 1. Customs change slowly, but they change. Eric and I decided that we preferred to randomize over the order in which names appear on joint papers rather than adhere always to alpha- betic order.

References Arthur, W.B. (1994). Increasing Returns and Path Dependence in the Economy Ann Arbor Michigan. University of Michigan Press. Bak, P., Nørrelykke, S. F., & Shubik, M. (1999). Dynamics of money. Physical Review E, 60, 2528-2532. Bak, P., Paczuski, M., & Shubik, M. (1997). Experts, noise traders and fat tail distributions. Economics Notes, 26, 251-290. Black, F. (1970). A world without money. Journal of Banking Research, 1, 8-20. Brewer, G., & Shubik, M. (1979). The war game. Cambridge, MA: Harvard University Press. Hesse, H. (1968). The glass bead game [Translated from German]. New York, NY: Holt, Rinehart and Winston. (Original work published 1949) Huber, J., Shubik, M., & Sunder, S. (2010a). An economy with personal currency: Theory and experimental evidence. Annals of Finance, 6, 475-509. Huber, J., Shubik, M., & Sunder, S. (2010b). Three minimal market institutions with human and algorithmic agents: Theory & experimental evidence. Games and Economic Behavior, 70, 403-424. Kiyotaki, N., & Wright, R. (1989). On money as a medium of exchange. Journal of Political Economy, 97, 927-954. Powers, M. R., & Shubik, M. (August, 1999). Reinsurance and retrocession: Optimal configu- rations for an evolving market. Proceedings of the International Insurance Society Annual Seminar, Berlin, Germany.

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Powers, M. R., Shubik, M., & Yao, S. T. (1998). Insurance market games: Scale effects and public policy. Journal of Economics, 67, 109-134. Quint, T., & Shubik, M. (2013, forthcoming). Barley gold and fiat: A pure theory of money. New Haven, CT: Yale University Press. Sahi, S., & Yao, S. (1989). The non-cooperative equilibria of a trading economy with complete markets and consistent prices. Journal of Mathematical Economics, 18, 325-346. Schumpeter, J. A. (1934). The theory of economic development. Cambridge, MA: Harvard University Press. (Original work published 1911) Shubik, M. (1954). Readings in game theory and political behavior. New York, NY: Doubleday. Shubik, M. (1971). The dollar auction game: A paradox in noncooperative behavior and escala- tion. Journal of Conflict Resolution, 15, 109-111. Shubik, M. (1975a). Games for society, business and war. Amsterdam, Netherlands: Elsevier. Shubik, M. (1975b). The uses and methods of gaming. New York, NY: Elsevier. Shubik, M. (1979). On the Number of Types of Markets with Trade in Money: Theory and Possible Experimentation. In V. L. Smith (Ed.), Research in Experimental Economics. Connecticut, USA: JAI Press. Shubik, M. (1997). On the trail of a White Whale: The rationalizations of a mathematical institutional economist. In A. Heertje (Ed.), The makers of modern economics (Vol. 3, pp. 96- 121). London, UK: Edward Elgar. Shubik, M. (1999a). The theory of money and financial institutions (Vol. 1). Cambridge, MA: MIT Press. Shubik, M. (1999b). The theory of money and financial institutions (Vol. 2). Cambridge, MA: MIT Press. Shubik, M., Karatzas, L., & Sudderth, W. D. (1994). Construction of stationary Markov equilibria on a strategic market game. Mathematics of Operations Research, 19, 975-1006. Shubik, M., & Levitan, R. E. (1980). Market structure and behavior. Cambridge, MA: Harvard University Press. Shubik, M., & Smith, D. E. (2005). Strategic freedom, constraint and symmetry in one-period markets with cash and credit payment. Economic Theory, 25, 513-551. Shubik, M., & Sudderth, W. (2011). Cost innovation: Schumpeter and equilibrium. Part 1. Robinson Crusoe. Unpublished manuscript. Cowles Foundation Discussion Paper 1786. New Haven, CT, USA. Shubik, M., & Whitt, W. (1973). Fiat money in an economy with one nondurable good and no credit (A noncooperative sequential game). In A. Blaquiere (Ed.), Topics in differential games (pp. 401-448). Amsterdam, Netherlands: Elsevier. Smith, D. E., & Shubik, M. (2011). Money and the valuation of trade. Journal of Mathematical Economics, 47, 508-530. Somary, F. (1986). The Raven of Zurich: The memoires of Felix Somary (A. J. Sherman, Trans.). London, England: C. Hurst. Sorin, S. (1996). Strategic market games with exchange rates. Journal of Economic Theory, 68, 431-446. von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton, NJ: Princeton University Press. Whitt, W. (1975). Stationary equilibria in an economy with money, uncertainty, infinitely many time periods and a continuum of traders. Unpublished manuscript, Yale University, New Haven, CT.

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