Comonotonic Convex Preferences

2013 ◽  
Author(s):  
Jianming Xia
Keyword(s):  
Convex Preferences

scholarly journals Dynamic consistency, valuable information and subjective beliefs

2021 ◽  
Author(s):  
Spyros Galanis
Keyword(s):  
Value Of Information ◽  
Single Agent ◽  
Bayesian Updating ◽  
Dynamic Consistency ◽  
Decision Problems ◽  
Backward Induction ◽  
Subjective Expected Utility ◽  
Trading Behavior ◽  
Subjective Beliefs ◽  
Convex Preferences

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.

scholarly journals Arrovian Aggregation of Convex Preferences

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 799-844
Author(s):  
Florian Brandl ◽  
Felix Brandt
Keyword(s):  
Social Welfare ◽  
Complete Characterization ◽  
Choice Functions ◽  
Maximal Elements ◽  
The Social ◽  
Outcome Space ◽  
Convex Preferences ◽  
Finite Set ◽  
Arrovian Aggregation

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.

scholarly journals Continuous mean demand functions derived from non-convex preferences

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

scholarly journals Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

2019 ◽  
Vol 4 (2) ◽  
pp. 331-350 ◽  
Author(s):  
Dushko Josheski ◽  
Elena Karamazova ◽  
Mico Apostolov
Keyword(s):  
Convex Sets ◽  
Probability Distributions ◽  
Equilibrium Price ◽  
Statistical Distributions ◽  
Lyapunov Theorem ◽  
Asymmetric Auctions ◽  
Convex Preferences

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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