Comonotonic Convex Preferences

Author(s):  
Jianming Xia
Keyword(s):  
Author(s):  
Spyros Galanis

AbstractAmbiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior.


Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 799-844
Author(s):  
Florian Brandl ◽  
Felix Brandt

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.


1980 ◽  
Vol 7 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Egbert Dierker ◽  
Hildegard Dierker ◽  
Walter Trockel

2019 ◽  
Vol 4 (2) ◽  
pp. 331-350 ◽  
Author(s):  
Dushko Josheski ◽  
Elena Karamazova ◽  
Mico Apostolov

AbstractIn this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.


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