The History Of Game Theory, Volume 1: From the Beginnings to 1945 (Routledge Studies in the History of Economics)

The History Of Game Theory, Volume 1: From the Beginnings to 1945 (Routledge Studies in the History of Economics)

Mary-Ann Dimand, Robert W Dimand

Language: English

Pages: 200

ISBN: 0415072573

Format: PDF / Kindle (mobi) / ePub

Game Theory - the formal modelling of conflict and cooperation - first emerged as a recognized field with a publication of John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behaviour in 1944. Since then, game-theoretic thinking about choice of strategies and the interdependence of people's actions has influenced all the social sciences. However, little is known about the history of the theory of strategic games prior to this publication.
In this volume, the history of strategic games - from its origins up to 1945 - is traced through the work of:
* 19th Century economists such as Cournot and Edgeworth
* Voting theorists - including Lewis Carroll
* Conflict theorists - Richardson and Lanchester
* Probabilists such as Bertrand, Borel and Ville
* Later economists - notably Stackelberg and Zeuthen
This authoritative account of the history of game theory concludes with a historical perspective on the achievement of von Neumann and Morgenstern, and an appraisal of the reception of their book.













Behavior’, in E.R. Weintraub (ed.) Toward a History of Game Theory, Durham, NC: Duke University Press, annual supplement to History of Political Economy vol. 24, 77–93. *Richardson, L.F. (1919) The Mathematical Psychology of War, Oxford: W.Hunt. ——(1935a) ‘Mathematical psychology of war’, Nature vol. 135, 830–1. ——(1935b) ‘Mathematical psychology of war’, Nature vol. 136, 1025. ——(1938) ‘The arms race of 1909–13’, Nature vol. 142, 792–3. ——(1939) Generalized Foreign Politics, Cambridge: Cambridge

income, the results would be entirely different, and would not differ, so far as consumers are concerned, from those in treating of a monopoly. (1838, 79–80) That is, in modern terms, where the two producers can come to a binding agreement to maximize joint profit, the game becomes a cooperative one, and consumers face the monopoly price and joint output. The remaining gametheoretic problem, not addressed by Cournot, is the producer’s division of profits. 21 COURNOT AND DUOPOLY Cournot then

representing their prices as generally lower than their competitor’s. Still, since the game sketched by Borel is a one-shot game, no longer run effects due to reputation or customer loyalty which might be gained by such a policy can operate. Moreover, the rationale behind a constraint which sets each merchant’s ‘sacrifice’ at an identical value D is puzzling. Consequently Borel’s two-merchant game is less compelling than a Cournot or ‘Bertrand’ market game. Nonetheless, Borel’s suggestion that

equilibrium, discrete mathematics. Morgenstern was not attracted by more chimerical approaches to economics dressed up in mathematical garb such as business cycle forecasting based on fixed periodicities, Major Douglas’ A+B theorem of Social Credit, or Creedy’s 1934 Econometrica paper explaining economic fluctuations by rigid analogy to Newton’s laws of mechanics (assuming, for example, that at constant times the rate of acceleration of spending equals the unspent balance of income, in analogy

they have jointly produced and set the price accordingly. Neither way of arriving at the price, given output, seems thoroughly satisfactory. 7 Conversely, where what is exchanged for spring water is to some extent indivisible, multiple equilibria result. Suppose the smallest unit of money to be one centime, and call the two price-competing duopolists A and B. There are three types of equilibria: 1 A and B each set a price of zero centimes; 2 A (or B) sets a price of zero centimes, while B (or

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