Published by EH.NET (October 2008)

Jean-Philippe Touffut, editor, *Augustin Cournot: Modelling Economics*. Cheltenham, UK: Edward Elgar, 2007. xv + 148 pp. $90 (hardcover), ISBN: 978-1-84720-586-5.

Reviewed for EH.NET by Martin Shubik, Department of Economics, Yale University.

In the early 1950s, when I was a graduate student at Princeton, I had two academic heroes. They were Cournot and Edgeworth (in my lesser Pantheon were Jevons and Walras). As soon as John Nash discussed his thesis on noncooperative games with me, I pointed out to him that his solution which was mathematically highly general was in essence the one that Cournot had applied to economics and had presented in his great book of 1838. The solution called for individual mutually consistent expectations. At that time game theory in either cooperative or noncooperative form was virtually ignored in economics. It seemed to me that this natural extension of Cournot, whose work was unknown to Nash, was going to extend the scope of oligopolistic studies considerably. Nash and I were joined by John Mayberry in writing an article accepted by *Econometrica* (?A Comparison of Treatments of a Duopoly Situation,? 1953, 141-54.) This, I believe was the first treatment of oligopoly expanding on Cournot?s work utilizing modern game theory. The mathematical tools were being forged to expand vastly the noncooperative equilibrium methods to economics so brilliantly started by Cournot.

This book edited by the Director of the Cournot Center, Jean-Philippe Touffut, contains an introduction and seven contributions honoring Cournot and his contributions to modeling in economics.

Jean Magnan de Bornier?s essay is devoted to Cournot as an economist. He notes the considerable gap between the presentation and acceptance of Cournot?s models. It was towards the end of his life that Cournot noted that ?mon minuscule? was finally being understood by young economists such as Jevons and Walras. In 1881 Bertrand wrote a highly negative review, based essentially on the empirical question of whether the prime strategic variable should be price rather than quantity. Game theoretic understanding of the strategic form has shown that both can be cleanly mathematized, as can be models involving various levels of substitutability and complementarity among goods and services.

Thierry Martin deals with Cournot?s probabilistic epistemology. He stresses the diversity of Cournot?s interests, but deals in particular with Cournot?s interests in the basic foundations of probability. He notes Cournot?s concern both about the objective and subjective significance of probabilities. Cournot noted it ?sometimes pertains to a certain measurement of our knowledge, and sometimes to a measurement of the possibility of things, independently of the knowledge we have of them.? This essay also notes his concern for the use of statistics in economics.

Bernard Walliser deals with the functions of economic models. He suggests six: 1. the iconic; 2. the syllogistic; 3. the empirical; 4. the heuristic; 5. the pragmatic; and 6. the rhetorical function. Under these headings (explained in the text) Walliser evaluates Cournot?s considerable contributions with a stress on the use of mathematics in economic application. Walliser also notes Cournot?s concern about the misuse of formalism.

Glen Shafer discusses ?From Cournot?s Principle to Market Efficiency.? Cournot?s principle states that an event of small or zero probability singled out in advance will not happen! This is considered in terms of the developments of probability theory over the last century. The discussion is devoted to considering open partial equilibrium models without bankruptcy as applied to finance. Shafer claims to deal with competition and efficiency, but he covers only a narrow partial equilibrium aspect of finance and omits the considerable literature on oligopoly and open and closed economic models based on variants of Cournot?s model.

Robert Aumann?s Nobel address is essentially reproduced with some editing and no references whatsoever to Cournot and his work.

Robert Solow discusses Cournot and the social income. He notes the two chapters in Cournot that can be regarded as containing preliminary remarks pertaining to the mathematization of a closed equilibrium model are somewhat disappointing in their discussion of social income and do not provide much of a link to macroeconomics, as is indicated by Cournot?s inadequate consideration of the distinction between annual sales and final consumption.

The last essay is by Alain Desrosiers on comparing the incomparable: the sociology of statistics. He contrasts the approach of Adolphe Quetelet with that of Cournot, noting that Quetelet was an advocate of national offices of statistics, with that of Cournot who was more concerned with the theoretical foundations of statistics than the practical use of economic statistics.

I read this book with highly mixed reactions. As Cournot is one of my academic heroes I look forward to any celebration of his contributions. This collection presents a mixture. The articles of de Bornier, Walliser and Solow cover Cournot?s role as an economist including both his strengths and weaknesses. However, to some extent, they do not do full justice to the considerable influence of his work on game theory and its applications to economics.

The articles by Martin, Shafer and Derosieres are addressed to the study of Cournot the probability theorist and statistician.

The prize talk of Aumann on war and peace is out of context and does not belong in this book. It does not pertain to the topic at hand. A far more appropriate reprint would have been ?Markets with a Continuum of Traders,? *Econometrica* 32 (1964), 39-50.

In the opinion of this reviewer Cournot not only was a mathematician and probabilist, he was an excellent modeler linking the economic world with basic abstract models. Not mentioned in this book on modeling economics is the enormous proliferation of works based on Cournot?s modeling and application of a mutually consistent expectations model to oligopoly and economic competition. Among those clearly influenced have been, Aumann, Dubey, Geanakoplos, Mas-Collel, Shapley, Shell, Shubik, Tirole and many others.

Martin Shubik is Seymour Knox Professor of Mathematical Institutional Economics (emeritus) at Yale University. Among his twenty books and over two hundred articles are *Readings in Game Theory and Political Behavior* (New York: Doubleday, 1954) and *The Theory of Money and Financial Institutions* (MIT Press, 2004 and forthcoming, three volumes).