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Academic Commons Search Resultsen-usAmbiguity, measurability and multiple priors
http://academiccommons.columbia.edu/catalog/ac:116241
Amarante, Massimilianohttp://hdl.handle.net/10022/AC:P:505Thu, 24 Mar 2011 00:00:00 +0000The paper provides a notion of measurability which is suited for a class of Multiple Prior Models. Those characterized by nonatomic countably additive priors. Preferences generating such representations have been recently axiomatized in [12]. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci [8]. In addition, the paper contains a thorough description of the basic properties of the family of measurable/unambiguous sets, of the measure defined on those and of the dependence of the class of measurable sets on the set of priors. The latter is obtained by means of an application of Lyapunov's convexity theorem.Economic theoryma734EconomicsWorking papersEquivalence of public mixed-strategies and private behavior-strategies in games with public monitoring
http://academiccommons.columbia.edu/catalog/ac:116333
Amarante, Massimilianohttp://hdl.handle.net/10022/AC:P:509Thu, 24 Mar 2011 00:00:00 +0000In repeated games with public monitoring, the consideration of behavior strategies makes relevant the distinction between public and private strategies. Recently, Kandori and Obara [5] and Mailath, Matthews and Sekiguchi [7] have provided examples of games with equilibrium payoffs in private strategies which lie outside the set of Public Perfect Equilibrium payoffs. The present paper focuses on another distinction, that between mixed and behavior strategies. It is shown that, as far as with mixed strategies one is concerned, the restriction to public strategies is not a restriction at all. Our result provides a general explanation for the findings of Kandori and Obara [5] and Mailath, Matthews and Sekiguchi [7] as well as a general method for constructing examples of that sort.Economic theoryma734EconomicsWorking papersOn the uniqueness of convex-ranged probabilities
http://academiccommons.columbia.edu/catalog/ac:116218
Amarante, Massimilianohttp://hdl.handle.net/10022/AC:P:504Thu, 24 Mar 2011 00:00:00 +0000We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 < P(A∗) < 1 such that P(A∗) = P(B)=⇒ Q(A∗) = Q(B) whenever B∈Σ] is equivalent to the condition [∀A,B ∈ Σ P(A) > P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q.Economic theoryma734EconomicsWorking papersAmbiguous events
http://academiccommons.columbia.edu/catalog/ac:116095
Amarante, Massimilianohttp://hdl.handle.net/10022/AC:P:499Thu, 24 Mar 2011 00:00:00 +0000We focus on a class of Multiple Prior Models. Those characterized by nonatomic countably additive priors. Preferences generating such representations have been recently axiomatized in [17]. We argue that this is the proper setting for comparing the notions of unambiguous event given by Epstein and Zhang in [7] and by Ghirardato, Maccheroni and Marinacci in [10]. The two definitions are known to be nonequivalent. Our main result is that an event T is unambiguous in the sense of Epstein and Zhang if and only if either (i) it is unambiguous in the sense of [10]; or (ii) conditional on T, the decision maker is an expected utility maximizer. We also provide an easy operational criterion for establishing whether or not an event is unambiguous in the sense of Epstein and Zhang.Economic theoryma734EconomicsWorking papers