scholarly journals An explicit representation for disappointment aversion and other betweenness preferences

2020 ◽  
Vol 15 (4) ◽  
pp. 1509-1546
Author(s):  
Simone Cerreia-Vioglio ◽  
David Dillenberger ◽  
Pietro Ortoleva
Keyword(s):  
Functional Equation ◽  
Expected Utility ◽  
General Result ◽  
Explicit Representation ◽  
Implicit Representation ◽  
Utility Representation ◽  
Disappointment Aversion

One of the most well known models of non‐expected utility is Gul's (1991) model of disappointment aversion. This model, however, is defined implicitly, as the solution to a functional equation; its explicit utility representation is unknown, which may limit its applicability. We show that an explicit representation can be easily constructed, using solely the components of the implicit representation. We also provide a more general result: an explicit representation for preferences in the betweenness class that also satisfy negative certainty independence (Dillenberger 2010) or its counterpart. We show how our approach gives a simple way to identify the parameters of the representation behaviorally and to study the consequences of disappointment aversion in a variety of applications.

scholarly journals Why is the Duration of Imagined Walking Underproduced? A dual-representation view on the mental imagery of locomotion

2018 ◽  
Author(s):  
Naohide Yamamoto ◽  
Dagmara E. Mach ◽  
John W. Philbeck ◽  
Jennifer Van Pelt
Keyword(s):  
Mental Imagery ◽  
Temporal Structure ◽  
Explicit Representation ◽  
Production Task ◽  
Dual Representation ◽  
Implicit Representation ◽  
Time Production ◽  
Spatial Tasks ◽  
Motor Representations ◽  
Implicit Representations

Generally, imagining an action and physically executing it are thought to be controlled by common motor representations. However, imagined walking to a previewed target tends to be terminated more quickly than real walking to the same target, raising a question as to what representations underlie the two modes of walking. To address this question, the present study put forward a hypothesis that both explicit and implicit representations of gait are involved in imagined walking, and further proposed that the underproduction of imagined walking duration largely stems from the explicit representation due to its susceptibility to a general undershooting tendency in time production (i.e., the error of anticipation). Properties of the explicit and implicit representations were examined by manipulating their relative dominance during imagined walking through concurrent bodily motions, and also by using non-spatial tasks that extracted the temporal structure of imagined walking. Results showed that the duration of imagined walking subserved by the implicit representation was equal to that of real walking, and a time production task exhibited an equivalent underproduction bias as in imagined walking tasks that were based on the explicit representation. These findings are interpreted as evidence for the dual-representation view of imagined walking.

scholarly journals DISAPPOINTMENT AVERSION PREMIUM PRINCIPLE

2015 ◽  
Vol 45 (3) ◽  
pp. 679-702 ◽  
Author(s):  
Ka Chun Cheung ◽  
Wing Fung Chong ◽  
Robert Elliott ◽  
Sheung Chi Phillip Yam
Keyword(s):  
Economic Theory ◽  
Expected Utility ◽  
Translation Invariance ◽  
Regulatory Requirement ◽  
Behavioral Economic ◽  
Disappointment Aversion ◽  
Explicit Representations ◽  
Behavioral Economic Theory

AbstractIn recent years, the determination of premium principle under various non-expected utility frameworks has become popular, such as the pioneer works by Tsanakas and Desli (2003) and Kaluszka and Krzeszowiec (2012). We here revisit the problem under another prevalent behavioral economic theory, namely the Disappointment Aversion (DA) Theory proposed by Gul (1991). In this article, we define and study the properties of theDA premium principle, which builds on the equivalent utility premium principle. We derive various properties of this premium principle, such as non-negative and no unjustified risk loading, translation invariance, monotonicity, convexity, positive (non-)homogeneity, independent (non-)additivity, comonotonic (non-)additivity and monotonicity with respect to the extent of disappointment. A generalized Arrow–Pratt approximation is also established. Explicit representations of the premium principle are obtained for linear and exponential utilities, and they reveal that the premium principle proposed echoes the capital reserve regulatory requirement in practice.

scholarly journals On Koenigs' ratios for iterates of real functions

1969 ◽  
Vol 10 (1-2) ◽  
pp. 207-213 ◽  
Author(s):  
E. Seneta
Keyword(s):  
Functional Equation ◽  
General Result ◽  
Real Function ◽  
Real Solutions ◽  
Real Functions ◽  
Image Position ◽  
Schröder Functional Equation

In a recent note, M. Kuczama [5] has obtained a general result concerning real solutions φ(x) on the interval 0 ≦ x < a ≦∞ of the Schröder functional equation providing the known real function satisfies the following (quite weak) conditions: f(x) is continuous and strictly increasing in ([0 a);(0) = 0 and 0 <f(x) <x for x ∈ (0, a); limx→0+ {f(x)/x} = s; and f(x)/x is monotonic in (0, a).

Implicit and explicit representations of visual space

1999 ◽  
Vol 22 (5) ◽  
pp. 759-760
Author(s):  
Bruce Bridgeman
Keyword(s):  
Visual System ◽  
Visual Space ◽  
Explicit Representation ◽  
Implicit Representation ◽  
Implicit Information ◽  
Visible Object ◽  
Event Location ◽  
Explicit Representations ◽  
Implicit And Explicit ◽  
Alternative Decision

The visual system captures a unique contrast between implicit and explicit representation where the same event (location of a visible object) is coded in both ways in parallel. A method of differentiating the two representations is described using an illusion that affects only the explicit representation. Consistent with predictions, implicit information is available only from targets presently visible, but, surprisingly, a two-alternative decision does not disturb the implicit representation.

Field Theoretic Functional Calculus for the Anharmonic Oscillator in Low Approximations

1968 ◽  
Vol 23 (12) ◽  
pp. 1869-1887
Author(s):  
Wolfgang Schuler
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Test Problem ◽  
Infinite System ◽  
Anharmonic Oscillator ◽  
Explicit Representation ◽  
System Of Equations ◽  
Quantum Field ◽  
Functional Formulation ◽  
Technical Details

The theory of solution for quantum field functional equations as developped in II and III for a suitable test problem of quantum mechanics is investigated in low approximations. In Sect. 1 the functional formulation of the anharmonic oscillator is once more given and in Sect. 2 general translational equivalent functional equations. The expansion of the physical state functional into series of unsymmetrical and symmetrical base functionals and the representation of the functional equations for such expansions are discussed in Sect. 3. In the next Sect. 4 the unsymmetrical DYSON representation is investigated and the explicit representation of the smeared out functional equation by an infinite system of equations is derived. Then in Sect. 5 and 6 the system of equations is truncated for N = 3 and the corresponding eigenvalue equation is considered. The same is done in Sect. 7 and 8 for the HERWITTE representation. In the following Sect. 9 the original functional equation in a not smeared out form is treated in the DYSON representation and the corresponding system of unsymmetrized equations is given. Furthermore in Sect. 10 the N = 3 approximation together with other possibilities is investigated again. Finally the numerical results of our calculations for eigenvalues are stated and discussed. In the appendices technical details are derived.

scholarly journals Application of bionic models for situation management

2020 ◽  
Author(s):  
Olga Gerget ◽  
Nataliia Markova
Keyword(s):  
State Transition ◽  
Data Representation ◽  
Explicit Representation ◽  
Control Action ◽  
Multidimensional Data ◽  
System State ◽  
Implicit Representation ◽  
Control Actions ◽  
Python Programming ◽  
Time Information

The article discusses the concept of choosing the sequence of control actions in order to minimize the possibility of the system state transition to an adverse one. For this purpose, the bionic model based on the synthesis of information approach, neural networks and a genetic algorithm is developed. The functionality of each of the model elements and their interaction are presented in this paper. Special attention is paid to neuroevolutionary interaction. At the same time, information about control actions is encapsulated in the gene, which allowed increasing the functionality of the algorithm due to multidimensional data representation. The article describes the principle of data representation in bionic models, which differs from the existing ones by the possibility of explicit or implicit representation of the control action in the chromosome. In the explicit representation one neural network is formed, it describes the effect of any of the control actions involved in the training. An implicit view creates a set of models, each of which describes the effect of only one control action. A brief description of the software implemented in the Python programming language is provided.

Alternative Preferences

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Expected Utility ◽  
Ambiguity Aversion ◽  
Marginal Utility ◽  
Knightian Uncertainty ◽  
Stochastic Discount Factor ◽  
Ellsberg Paradox ◽  
First Order ◽  
Weighted Utility ◽  
Disappointment Aversion ◽  
Rank Dependent Utility

The Allais and Ellsberg paradoxes are presented. Various generalizations of expected utility motivated by these and other paradoxes are discussed, including betweenness preferences, rank‐dependent preferences, multiple prior max‐min preferences, and prospect theory. For betweenness preferences, which include weighted utility and disappointment aversion, an investor’s marginal utility is proportional to a stochastic discount factor. Disappointment averse utility and rank‐dependent utility have first‐order risk aversion. Multiple prior max‐min utility is one way to accomodate the Ellsberg paradox (ambiguity aversion or Knightian uncertainty). The dynamic consistency of updating multiple priors is discussed.

Coalitional Expected Multi‐Utility Theory

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 933-980 ◽  
Author(s):  
Kazuhiro Hara ◽  
Efe A. Ok ◽  
Gil Riella
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Preference Relation ◽  
Revealed Preference ◽  
Portfolio Diversification ◽  
Independence Axiom ◽  
Representation Theorems ◽  
Utility Representation ◽  
Reversal Phenomenon ◽  
Preference Reversal Phenomenon

This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision‐maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

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