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Decision Making under Extreme Uncertainty

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Topic: Decision Making

Sort Desciption: The current paper investigates decision making in environments of extreme ..... Up to this point we were only concerned with decision making in an informa- ...

Content Inside: Decision Making under Extreme Uncertainty Michael Schwarz Harvard University Department of Economics and Hoover Institution at Stanford Abstract Beliefs about an unknown distribution can be defined as a measure on the space of probability density functions. This paper (1) characterizes the set of beliefs that satisfy invariance postulates (2) establishes that updating invariant beliefs leads to a posterior distribution with tail asymptotically approaching 1 x(ln x) n . Note to seminar participant at Wharton: Part I of this paper is primarily of interest to economic theorists. Part II may be of interest to statisticians hence you may want to skip the first dozen pages. I am grateful to Kenneth Arrow Jeremy Bulow Darrell Duffie Edward Lazear Ilya Segal and Robert Wilson. Also I would like to thank E. Dahan L. Mirny and M. Yildiz. Send correspondence to Michael Schwarz Economics Department Harvard Univeristy Cambridge MA 02138 Email: mschwarz@harvard.edu 1. Introduction The current paper investigates decision making in environments of extreme uncer- tainty. We use invariance principles to derive restrictions on an agents behavior. According to invariance principles an agent treats the units of measurement as an uninformative label. For instance a broker can perform calculations in dol- lars or in cents but resulting decision to buy or sell should not depend on the choice of the measurement scale. The class of decision problems considered in the current work can be illustrated by the following example. In 1986 scientists at IBM Zurich research laboratories discovered high temperature superconductors. A numerical measure of a superconductor performance is the maximum current that it can sustain. The earliest high-temperature superconductors deliver per- formance below the threshold of practical usability. Furthermore a number of projects are complementary to the advancement in high-temperature supercon- ductor technology if the performance of high ...

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