/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Impatti, adattamento e vulnerabilita Le cause e le responsabilita dei cambiamenti climatici sono state trattate sul numero di ottobre della rivista Cda. Approfondiamo l’argomento presentando il documento: “Cambiamenti climatici 2007: impatti, adattamento e vulnerabilita” votato ad aprile 2007 dal secondo gruppo di lavoro del Comitato Intergovernativo sui Cambiamenti Climatici (Intergovernmental Panel on Climate Change). Si tratta del secondo di tre documenti che compongono il quarto rapporto sui cambiamenti climatici.

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Climate Change 2007: Impacts, Adaptation and Vulnerability.

Information Theory and Reliable Communication

The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

A Borel probability measure is residual if it gives measure zero to all meager subsets. We first give some existence results about this class of measures. Then they are applied in order to get some non-existence results for probability measures defined on Boolean algebras. This is done on the basis of some duality methods. Finally we prove that the range of a nonatomic probability measure defined on a Boolean algebra which satisfies the c.c.c. is dense in the unit inter val.

Residual Measures and the Existence and Range of Probability Measures n Boolean Algebras

We consider an uncertainty averse, sophisticated decision maker facing a recurrent decision problem where information is generated endogenously. In this context, we study self-confirming strategies as the outcomes of a process of active experimentation. We provide inter alia a learning foundation for self-confirming equilibrium with model uncertainty (Battigalli et al., 2015). We also argue that ambiguity aversion tends to stifle experimentation, increasing the likelihood that decision maker get stuck into suboptimal certainty traps.

Learning and Self-confirming Long-Run Biases

We consider a game with sequential moves played by agents who are randomly drawn from large populations and matched. We assume that, when players are uncertain about the strategy distributions of the opponents, preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005). This may induce dynamically inconsistent preferences and calls for an appropriate definition of sequential best response. We take this into account in our analysis of self-confirming equilibrium (SCE) and rationalizable SCE in sequential games with feedback played by agents with non-neutral ambiguity attitudes. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for (rationalizable) SCE. Keywords: Sequential games with feedback, smooth ambiguity, self-confirming equilibrium, rationalizable self-confirming equilibrium.

Ambiguity Attitudes and Self-Confirming Equilibrium in Sequential Games

A coalitional game is a real-valued set function v defined on an algebra F of subsets of a space X such that v(0)=0. We prove the existence of a one-to-one correspondence between coalitional games bounded with respect to the composition norm and countably additive measures defined on an appropriate space.

Massimo Marinacci

Papers

Residual Measures and the Existence and Range of Probability Measures n Boolean Algebras

Learning and Self-confirming Long-Run Biases

Ambiguity Attitudes and Self-Confirming Equilibrium in Sequential Games

Decomposition and Representation of Coalitional Games

Notes, Comments, and Letters to the Editor Mutual absolute continuity of multiple priors