Abstract
Unlike many of the papers at this Conference, this paper concerns games against nature rather than games against strategically-motivated human (or computer) opponents. Nevertheless, games against nature are relevant to games against opponents - as the literature makes clear. Indeed, one of the seminal pieces of that literature, John von Neuman/Oskar Morgenstern, The Theory of Games and Economic Behaviour (1947)1, whilst ostensibly addressed to the theory of strategic games, derived one of the key elements of the theory of rational decision making against nature — namely Expected Utility theory — as a key component of the theory of strategic games. Moreover, many of the interesting new developments in Game Theory are pursuing the implications of non-Expected-Utility behaviour in games Contrariwise, some recent developments in individual decision-making, such as those related to intertemporal decision-making, are using results from the theory of games. Clearly, developments in each branch of the literature are relevant to the other branch.
I am grateful to the organisers of the Conference for inviting me to Vienna, and for organising an extremely interesting conference in which the most fruitful feature was the bringing together of experts from different disciplines.
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Notes
John von Neuman/Oskar Morgenstern, The Theory of Games and Economic Behaviour, Princeton: Princeton University Press, 1947
With the exception of Yaari’s Dual theory and the possible exception of the (original) version of Prospect theory.
This can be so under Quadratic Utility theory (see Soo Hong Chew/Larry Epstein/Uzi Segal, “Mixture Symmetry and Quadratic Utility” in Econometrica 59, 1, 1991, pp.139–163).
There is an interesting philosophical point here: suppose the individual recognises all of this, carries out the randomisation - and that P is the consequence. Could one argue - as Machina invites us to do - that the individual ought to carry out the randomisation again, since the individual prefers the mixture to P? This line of argument seems to lead to inaction rather than action!
See, for example, Duncan Luce, “A Probabilistic Theory of Utility”, in: Econometrica 26, 1, 1958, pp 193–224.
John Hey and Christopher Orme, “Investigating Generalisations of Expected Utility Theory Using Experimental Data”, in Econometrica,62, 6, 1994, pp.1291–1326.
The order of the questions was randomly chosen on each occasion, and the position of the left and right choices was reversed on the second occasion.
Enrica Carbone/John Hey, “A Comparison of the Estimates of EU and non-EU Preference Functionals Using Data from Pairwise Choice and Complete Ranking Experiments”, in: Geneva Papers on Risk and Insurance Theory 20, 2, 1995, pp.111–133
Parker Ballinger/Nat Wilcox “Decisions, Error and Heterogeneity”, University of Houston discussion paper, 1996.
Except in very rare cases.
Though was not the case in an early experiment by Kenneth MaCrimmon and Stig Lars, “Utility Theory: Axioms versus `Paradoxes—, in Marice Allais/Ole Hagen, Expected Utility and the Allais Paradox. Dordrecht: Reidel, 1979, pp. 333–409.
David Harless/Colin Camerer “The Predictive Utility of Generalized Expected Utility Theories”, in: Econometrica 62, 6, 1994, pp.1251–1290.
See John Hey, “Reconciling Harless and Camerer and Hey and Orme”, discussion paper, University of York, 1996.
An even better approximation is when the variance of the error term a is not assumed to be constant, but rather a function of what appears to be a measure of the complexity of the decision problem facing the subject. See John Hey, “Experimental Investigations of Errors in Decision Making under Risk”, in European Economic Review 39, 4, 1995, pp. 633–640.
Mark Machina, “Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries”, in: Economic Journal 95, 379, 1985, pp.575–594.
See endnote 3.
John Hey/Enrica Carbone, “Stochastic Choice with Deterministic Preferences: An Experimental Investigation”, in: Economics Letters,47, 2, 1994, pp.161–167.
Indeed so much so that we now wonder why we gave the subjects the option: it clearly does not increase their utility, since, if they are genuinely indifferent, there is no advantage to them in saying so; and it certainly does not help us because we cannot be sure - for the reason noted above - that the cases when they reported indifference were indeed the only cases when indifference was experienced. Furthermore, there is a serious problem in terms of most of the stories we are trying to fit - in that the probability of them being exactly indifferent is clearly zero.
Graham Loomes/Bob Sugden, “Incorporating a Stochastic Element into Decision Theories”, in: European Economic Review 39, 4, 1995, pp.641–648.
JOHN D. HEY
Enrica Carbone, “Estimation of Stochastic Utility Theory using Experimental Data”, paper presented at the Naples Experimental Economics conference, 1996.
21. An alternative measure is the value b such that V(P) = V(Q+b). Clearly a .and. 0 if and only if b .and. O.
Actually, a proper `theory of errors’ would recognise that error-making is (necessarily) stochastic - which means that the above discussion should be formulated in stochastic terms. However, this rather informal treatment is sufficient for my present purposes.
See Vernon Smith/James Walker, “Monetary Rewards and Decision Cost in Experimental Economics”, Economic Inquiry 31, 2, 1993, pp.245–261, for an apparently conflicting view.
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Hey, J.D. (1998). Do Rational People Make Mistakes. In: Leinfellner, W., Köhler, E. (eds) Game Theory, Experience, Rationality. Vienna Circle Institute Yearbook [1997], vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1654-3_5
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