Vivian, Robert William (2003): Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was. Published in: South African Journal of Economic & Management Sciences , Vol. 2, No. NS6 (2003): pp. 331-345.
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It has been accepted for over 270 years that the expected monetary value (EMV)of the St Petersburg game is infinite. Accepting this leads to a paradox; no reasonable person is prepared to pay the predicted large sum to play the game but will only pay, comparatively speaking, a very moderate amount. This paradox was 'solved' using cardinal utility. This article demonstrates that the EMV of the St Petersburg game is a function of the number ofgames played and is infmite only when an infinite number of games is played. Generally, the EMV is a very moderate amount, even when a large number of games is played. It is of the same order as people are prepared to offer to play the game. There is thus no paradox. Cardinal utility is not required to explain the behaviour of the reasonable person offering to play the game.
|Item Type:||MPRA Paper|
|Institution:||University of the Witwatersrand|
|Original Title:||Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was|
|Keywords:||St Petersburg paradox; St Petersburg game; expected utility; decision theory|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty|
|Depositing User:||Robert W Vivian|
|Date Deposited:||09. Oct 2007|
|Last Modified:||07. Jan 2014 19:59|
AASE, K.K. (2001) "On the St Petersburg Paradox", Scandinavian Actuarial Journal: 69-78. ALLAIS, M. (1979) "The Allais 1952 Theory of Choice with Uncertainty" in Expected Utility Hypotheses and the Allais Paradox, M Allais and 0 Hagen (eds.) Dordrecht, D Reidel Publishing Company. ALLAIS, M. & HAGEN, O. (1979) (eds.) Expected Utility Hypotheses and the Allais Paradox, Dordrecht, D Reidel Publishing Company. ARROW, K.J. (1951) "Alternative approaches to the theory of choice in risk-taking situations", Econometrica, 19: 404-37. ARROW, K.J. (1974) Essays in the Theory of Risk-Bearing, NorthHolland (2nd printing). BASSETT, G.W. (1984) "The St Petersburg paradox and bounded utility", History ofPolitical Economy, 19(4): 517-23. BERNOULLI, D. (1954/1738) "Exposition of a new theory on the measurement of risk" Econometrica, 22(1): 23-36. BERNSTEIN, P.L. (1998) Against the Gods - the remarkable story ofrisk, John Wiley & Sons BORCH, K.H. (1972/1968) The Economics of Uncertainty, Princeton: Princeton University Press (1968] 1972 reprinting. BRITO, D.L. (1975) "Becker's Theory of the Allocation of Time and the St Petersburg Paradox" Journal ofEconomic Theory, 10(1): 123-6. COWEN, T. & HIGH, J. (1988) "Time, bounded utility, and the St Petersburg Paradox", Theory and Decision, 10: 219-23. EPPS, T.W. (1978) "Financial Risk and the St Petersburg Paradox: Comment" Journal ofFinance, 33: 1455-56. FRIEDMAN, M. & SAVAGE, L. (1948) "The Utility analysis of choice involving risk", The Journal ofPolitical Economy, 56: 279-304. GOROVITZ, S. (1979) "The St Petersburg Puzzle" in Expected Utility Hypotheses and the Allais Paradox, M Allais and 0 Hagen (eds.) Dordrecht, D Reidel Publishing Company. KEYNES, J.M. (1973/1921) A Treatise on Probability, London: Macmillan Press Ltd, The Royal Economic Society Edition . MACHINA, MJ. (1987) "Choice under uncertainty: Problems solved and unsolved" Journal ofEconomic Perspectives, 1: 121-54. MARSHALL, A (1920) Principles of Economics (8th ed.) MacMillan & Co, London 1947 reprint. MENGER, K. (1954) in Bernoulli, Daniel. (1954/1738) "Exposition ofa new theory on the measurement ofrisk", Econometrica, 22: 23-36. RABIN, M. & THALER, R.H. (2001) "Anomalies: Risk aversion", The Journal ofEconomic Perspectives, 15: 219-32. RUSSON, M.G. & CHANG, SJ. (1992) "Risk aversion and practical expected value: A simulation of the St Petersburg Game", Simulation & Gaming, 23: 6-19. SAMUELSON, P.A. (1960) "The St Petersburg Paradox as a divergent double limit", International Economic Review, I: 31-7. SAMUELSON, P.A. (1977) "St Petersburg Paradoxes: Defanged,dissected and historically described", Journal ofEconomic Literature, 15: 24-55. SAVAGE, L.J. (1972) The Foundations ofStatistics, (2nd ed.) New York, Dover Publications Inc. (rev. ed.) SENNE'ITI, J. (1976) "On Bernoulli, Sharpe, financial risk and the St Petersburg Paradox", The Journal ofFinance, 31: 960-62. SCHMEIDLER, D. & WAKKER, P. (1996) "Expected utility and mathematical expectation", The New Palgrave - A dictionary of Economics, MacMillan Press: 229. SCHOEMAKER, PJ.H. (1982) ''The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations", Journal of Economic Literture, 20: 529-36. SHAPLEY, L.S. (1977) ''The St Petersburg Paradox: A con game", Journal ofEconomic Theory, 10: 439-42. STARMER, C. (2000) "Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk", Journal ofEconomic Literature, 38(2): 332-82. STIGLER, G.J. (1950) "The development of utility theory II", The Journal ofPolitical Economy, 58: 373-96. SZEKELY, G.J. (1986) Paradoxes in Probability Theory and Mathematical Statistics, Dordrecht, D Reidel Publishing Company. TODHUNTER, I. (1949/1865) A History ofthe Mathematical Theory of Probability - from the time of Pascal to that of Laplace, New York: Cambridge University Press 1865. Reprint. New York: Chelsea Publishing Company. VON NEUMANN, J. & MORGENSTERN, O. (1953) The Theory of Games and Economic Behaviour (3ro ed.) Princeton. Princeton University Press.