Two Fields Medalists Contributions to Economic Theory (December, 16th, 2010)

Why mathematicians have interest in Economics?  To be read:

Economics as a Minor for Undergraduate Mathematics Majors, The American Mathematical Monthly, Vol. 80, No. 6 (Jun. - Jul., 1973), pp. 688-689, by Ellis.

 John Milnor (1962 Medalist)

           Milnor’s contributed to Economic Theory basically in Game  Theory with subjects like Games against Nature, Experimental n-Person Games, and On Games of Survival. Also, an axiomatic approach to measurable utility as we know sourced from Arrow-Debreu general equilibrium model.

Basic References:

           

An axiomatic approach to measurable utility, (with I.N. Herstein), Econometrica 21  (1953), pp 291-297.

Sums of positional games in “Contributions to the Theory of Games, Vol. II” (H. W. Kuhn and A.W. Tucker, eds.), Ann. of Math. Stud. No. 28, Princeton University Press, Princeton, N.J., 1953, pp. 291-301.

Games against nature, in “Decision Processes,” (R. M. Thrall, C.H. Coombs and R.L.Davis, eds.) Wiley, New York; Chapman and Hall Ltd., London, 1954, pp. 49-59.

Some experimental n-person games, (with G. Kalish, J. Nash, and E.D. Nering),  “Decision Processes,” (R. M. Thrall, C.H. Coombs and R.L.Davis, eds.) Wiley, New York; Chapman and Hall Ltd., London, 1954,, pp. 301-327.

On games of survival, (with L.S. Shapley), in “Contributions to the Theory of Games, Vol. III,” (M. Dresher, A.W. Tucker and P. Wolfe, eds.), Ann. of Mth. Stud. No. 39, Princeton University Press, Princeton, N.J. 1957, pp. 15-45

 Steve Smale (1966 Medalist)

            Smale’s contributions are in Microeconomic Theory and an isolated Game Theory contribution on prisoner’s dilemma dynamic. Different from Milnor,  Smale’s works in economics happened after Fields Medal event. As a matter of fact his attention was toward global analysis and general equilibrium dynamic with contributions published in important economics journals (Econometrica, American Economics Review, and mainly Journal of Mathematical Economics). 

Basic References:

Global analysis and economics, I: Pareto Optimum and a generalization of Morse theory, Dynamical Systems, edited by M. M. Peixoto, Academic Press (1973).

Global analysis and economics, IIA, Journal of Mathematical Economics, First Issue, April 1974, pp. 1--14.

Global analysis and economics, III: Pareto Optima and price equilibria, Journal of Mathematical Economics, I (1974), pp. 107--117.

Global analysis and economics, IV: Finiteness and stability of equilibria with general consumption sets and production, Journal of Mathematical Economics, I (1974), pp. 119--127.

Global analysis and economics, V: Pareto theory with constraints, Journal of Mathematical Economics, I (1974), pp. 213--221.

Dynamics in general equilibrium the theory, American Economic Review, 66 (1976), pp. 288--294.

A convergent process of price adjustment, Journal of Mathematical Economics, 3 (1976), pp. 107--120.

Exchange processes with price adjustment, Journal of Mathematical Economics, 3 (1976), pp. 211--226.

The prisoner's dilemma and dynamical systems associated to non-cooperative games, Econometrica, 48 (1980), pp. 1617--1634.

Global analysis and economics, Handbook of Mathematical Economics, K. J. Arrow and M. D. Intrilligator, North-Holland, Amsterdam, 1 (1981), pp. 331--370.