1,721,055 research outputs found
Disputed Lands
No full textIn this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy free (and a fortiori fair) divisions of it into subsimplexes.
The main tool is an extension of a representation theorem of Gilboa and Schmeidler [Gilboa, I., Schmeidler, D., 1989, Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153]
A strong law of large numbers for capacities
No full textWe consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous
Linear Functionals Preserving a Given Preorder with an Application to the Term Structure of Interest Rates
No full textDati non disponibil
Equilibria of nonatomic anonymous games
Full text linkWe define a new notion of equilibrium for nonatomic anonymous games, termed epsilon-estimated equilibrium, and prove its existence for any positive s. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. Our approach also resolves some conceptual problems present in Schmeidler (1973) pointed out by Shapley
Ambiguity aversion and wealth effects
Full text linkWe study how changes in wealth affect ambiguity attitudes. We define a decision maker as decreasing (resp., increasing) absolute ambiguity averse if he becomes less (resp., more) ambiguity averse as he becomes richer. Our definition is behavioral. We provide different characterizations of these attitudes for a large class of preferences: monotone and continuous preferences which satisfy risk independence. We then specialize our results for different subclasses of preferences. Inter alia, our characterizations provide alternative ways to test experimentally the validity of some of the models of choice under uncertainty
Orthogonal decompositions in Hilbert A-modules
No full textPre-Hilbert A-modules are a natural generalization of inner product spaces in which the scalars are allowed to be from an arbitrary algebra. In this perspective, submodules are the generalization of vector subspaces. The notion of orthogonality generalizes in an obvious way too. We provide necessary and sufficient topological conditions for a submodule to be orthogonally complemented. Then, we present four applications of our results. The most important ones are Doob's and Kunita–Watanabe's decompositions for conditionally square-integrable processes. They are obtained as orthogonal decomposition results carried out in an opportune pre-Hilbert A-module. Second, we show that a version of Stricker's Lemma can be also derived as a corollary of our results. Finally, we provide a version of the Koopman–von-Neumann decomposition theorem for a specific pre-Hilbert module which is useful in Ergodic Theory
Social decision theory: choosing within and between groups
No full textWe study the behavioral foundation of interdependent preferences, where the outcomes of others affect the welfare of the decision maker. These preferences are taken as given, not derived from more primitive ones. Our aim is to establish an axiomatic foundation providing the link between observations of choices and a functional representation which is convenient, free of inconsistencies and can provide basis for measurement.
The dependence among preferences may take place in two conceptually different ways, expressing two different views of the nature of interdependent preferences. The first is Festinger's view that the evaluation of peers' outcomes is useful to improve individual choices by learning from the comparison. The second is Veblen's view that interdependent preferences keep track of social status derived from a social value attributed to the goods one consumes. Corresponding to these two different views, we have two different formulations. In the first the decision maker values his outcomes and those of others on the basis of his own utility. In the second, he ranks outcomes according to a social value function.
We give different axiomatic foundations to these two different, but complementary, views of the nature of the interdependence. On the basis of this axiomatic foundation we build a behavioral theory of comparative statics within subjects and across subjects. We characterize preferences according to the relative importance assigned to gains and losses in social domain, that is, pride
and envy. This parallels the standard analysis of private gains and losses (as well as that of regret and relief ). We give an axiomatic foundation of inter personal comparison of preferences, ordering individuals according to their sensitivity to social ranking. These characterizations provide the behavioral foundation for applied analysis of market and game equilibria with interdependent preferences
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