TY - JOUR

T1 - Calibrated uncertainty

AU - Gul, Faruk

AU - Pesendorfer, Wolfgang

N1 - Funding Information:
This research was supported by National Science Foundation grants SES-1426252 and SES-1729021 . We are grateful to Andrew Ferdowsian for comments and suggestions.
Publisher Copyright:
© 2020 Elsevier Inc.

PY - 2020/7

Y1 - 2020/7

N2 - We define a binary relation (qualitative uncertainty assessment) that describes the shared likelihood assessments of decision makers with diverse ambiguity attitudes. Ambiguity renders this binary relation incomplete. Our axioms yield a representation according to which A is more likely than B if and only if a capacity, called uncertainty measure, assigns a higher value to A than to B and a higher value to B-complement than to A-complement. Agents combine this uncertainty perception with their uncertainty attitude to form a complete ranking of bets. We provide a representation theorem for this extended model, show that its parameters are uniquely identified and characterize a new measure of comparative ambiguity aversion. For general acts, we modify Machina and Schmeidler's (1992) sophistication axiom to allow for ambiguity and analyze three nested extensions: first, we axiomatize a minimal extension which reduces to expected utility when there is no ambiguity; the second and third extensions show how non-expected utility theories can be accommodated in our framework.

AB - We define a binary relation (qualitative uncertainty assessment) that describes the shared likelihood assessments of decision makers with diverse ambiguity attitudes. Ambiguity renders this binary relation incomplete. Our axioms yield a representation according to which A is more likely than B if and only if a capacity, called uncertainty measure, assigns a higher value to A than to B and a higher value to B-complement than to A-complement. Agents combine this uncertainty perception with their uncertainty attitude to form a complete ranking of bets. We provide a representation theorem for this extended model, show that its parameters are uniquely identified and characterize a new measure of comparative ambiguity aversion. For general acts, we modify Machina and Schmeidler's (1992) sophistication axiom to allow for ambiguity and analyze three nested extensions: first, we axiomatize a minimal extension which reduces to expected utility when there is no ambiguity; the second and third extensions show how non-expected utility theories can be accommodated in our framework.

KW - Ambiguity

KW - Ambiguity measure

KW - Separation of ambiguity perception and ambiguity attitude

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U2 - 10.1016/j.jet.2020.105016

DO - 10.1016/j.jet.2020.105016

M3 - Article

AN - SCOPUS:85083064023

SN - 0022-0531

VL - 188

JO - Journal of Economic Theory

JF - Journal of Economic Theory

M1 - 105016

ER -