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The $$\alpha$$-MEU model: a comment. (English) Zbl 1247.91061
Summary: P. Ghirardato, F. Maccheroni and M. Marinacci [J. Econ. Theory 118, No. 2, 133–173 (2004; Zbl 1112.91021)] proposed a method for distinguishing between perceived ambiguity and the decision-maker’s reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of $$\alpha$$-MEU preferences. If attention is restricted to finite state spaces, we show that any $$\alpha$$-MEU preference relation, satisfies GMM’s axioms if and only if $$\alpha =0$$ or $$1$$, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is $$[0,1]$$.

##### MSC:
 91B16 Utility theory 91B06 Decision theory
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