Download or read book Continuous Preference Orderings Representable by Utility Functions written by Carlos Hervés-Beloso and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys the conditions under which it is possible to represent a continuous preference ordering using utility functions. We start with a historical perspective on the notions of utility and preferences, continue by defining the mathematical concepts employed in this literature, and then list several key contributions to the topic of representability. These contributions concern both the preference orderings and the spaces where they are defined. For any continuous preference ordering, we show the need for separability and the sufficiency of connectedness and separability, or second countability, of the space where it is defined. We emphasize the need for separability by showing that in any nonseparable metric space, there are continuous preference orderings without utility representation. However, by reinforcing connectedness, we show that countably boundedness of the preference ordering is a necessary and sufficient condition for the existence of a (continuous) utility representation. Finally, we discuss the special case of strictly monotonic preferences.
Download or read book Representations of Preferences Orderings written by Douglas S. Bridges and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a rigorous presentation of results about the representation of preference orderings by real-valued order isomorphisms ("utility functions"). The authors have gathered together, from sources scattered throughout a wide range of the literature of mathematics and economics, the most significant theorems and methods in their field. The book will be a valuable resource for theoretical economists, mathematicians, and all interested in partial orders and their representation. It could also be used as the text for an advanced graduate course in mathematical economics.
Download or read book Weakly Monotonic Preference Relations Representable by Concave Utility Functions It s Easy written by Somdeb Lahiri and published by . This book was released on 2017 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide conditions under which a preference relation can be represented by concave utility functions. The condition follows naturally from a proof of a theorem about representability of continuous and weakly monotonic preference relations by continuous and weakly increasing utility functions due to Wold (1943). For continuous and homothetic (hence weakly monotonic) preference relations our sufficient condition for the existence of a numerical representation by a concave utility function is also a necessary condition for such a numerical representation. In fact we are able to obtain a necessary condition for numerical representation of a homothetic preference relation by a concave utility function which we call global concavifiability and which is much stronger than concavifiability. On the way, we pick up the result, that all homothetic and continuous preference relations which are convex are numerically representable by concave utility functions.
Download or read book Mathematical Topics on Representations of Ordered Structures and Utility Theory written by Gianni Bosi and published by Springer Nature. This book was released on 2020-01-23 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential review of central theories, current research and applications in the field of numerical representations of ordered structures. It is intended as a tribute to Professor Ghanshyam B. Mehta, one of the leading specialists on the numerical representability of ordered structures, and covers related applications to utility theory, mathematical economics, social choice theory and decision-making. Taken together, the carefully selected contributions provide readers with an authoritative review of this research field, as well as the knowledge they need to apply the theories and methods in their own work.
Download or read book Utility Functions on Ordered Spaces written by and published by . This book was released on 1999 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Utility Maximization Choice and Preference written by Fuad Aleskerov and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.
Download or read book Continuous Representation of Preferences written by Graciela Chichilnisky and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of constructing a representation of preferences appears when it is needed to assign utility functions to preferences in a well-defined way, since in general many utilities will represent the same preference. In models where the preferences of the agents vary, and the behaviour of the model depends on limiting properties of preferences, it is important that utilities be assigned to preferences so as to vary continuously as preferences change. In this paper we study a utility representation for preferences, and we prove its continuity, using a topology for preferences introduced by Chichilnisky (1977). Such utility representations were constructed under restrictive conditions first by Y. Kannai (1970), W. Hildenbrand (1970), W. Neuefeind (1972) and more recently by K. Mount and S. Reiter (1974, 1975). Our results are related more closely to those of Mount and Reiter (1974 and 1975). Starting from restrictive conditions, these works have attempted to enlarge the class of preferences that could be continuously represented. The class of preferences studied here is much larger than those considered earlier, and it therefore applies to a wider class of problems. Our preferences include ones which are not necessarily convex or monotone, and which may be locally satiated; furthermore, no completeness of the preferences is required. The assumption made in Mount and Reiter (1975) of the existence of an ez-threshold is also not required here. These results are possible due to the properties of the order topology introduced in Chichilnisky (1977). As we shall now discuss, this topology has quite desirable features for the study of preferences, and these make it a natural choice for the problem at hand. The order topology is liner than the Hausdorlf metric, and, as opposed to the Hausdorff metric, it is sensitive to the measure of the graphs of the preferences. This sensitivity is the main property that allows one to prove continuity of the representation, which is based on measure.
Download or read book The Structure of Utility Functions written by Stanford University. Institute for Mathematical Studies in the Social Sciences and published by . This book was released on 1967 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: A continuous complete preference ordering is defined on an arcconnected, topologically separable product space S = S1xS2x.xSn. Call 1,.n sectors and say that a set A of sectors is separable if the conditional ordering on A, given what happens off it, is independent of the latter, essential if it matters what happens on A, at least sometimes, and strictly essential if it always does. It is shown how to determine the structure of the utility function, given a collection of separable sets, when each sector is strictly essential. Various examples are discussed, an alternative approach sketched, and, finally, the requirement of strict essentiality replaced by the basically nugatory condition that each sector be essential. The results can, of course, be applied to other functions, too. (Author).
Download or read book Preferences and the Dynamic Representative Consumer written by and published by . This book was released on 2005 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Preference Modelling written by Marc Roubens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following scheme summarizes the different families introduced in this chapter and the connections between them. Family of interval orders f Row-homogeneous Column-homogeneous Family of family of interval semi orders family of interval orders orders Homogeneous family of i nterva 1 orders Homogeneous family of semi orders Family of weak orders 85 5.13. EXAMPLES We let to the reader the verification of the following assertions. Example 1 is a family of interval orders which is neither row-homogeneous nor column-homogeneous. Example 2 is a column-homogeneous family of interval orders which is not row-homogeneous but where each interval order is a semiorder. Example 3 is an homogeneous family of interval orders which are not semiorders. Example 4 is an homogeneous family of semi orders . . 8 ~ __ --,b ~---i>---_ C a .2 d c Example Example 2 .8 .6 c .5 a 0 a d Example 3 Example 4 5.14. REFERENCES DOIGNON. J.-P •• Generalizations of interval orders. in E. Degreef and J. Van Buggenhaut (eds). T~ndS in MathematiaaZ PsyahoZogy. Elsevier Science Publishers B.V. (North-Holland), Amsterdam, 1984. FISHBURN. P.C., Intransitive indifference with unequal indifference intervals. J. Math. Psyaho.~ 7 (1970) 144-149. FISHBURN. P.C., Binary choice probabilities: on the varieties of stochastic transitivity. J. Math. Psyaho.~ 10 (1973) 327-352.
Download or read book Lecture Notes in Microeconomic Theory written by Ariel Rubinstein and published by Princeton University Press. This book was released on 2012-03-04 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ariel Rubinstein's well-known lecture notes on microeconomics—now fully revised and expanded This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics. Developed during the fifteen years that Rubinstein taught the course at Tel Aviv University, Princeton University, and New York University, these notes provide a critical assessment of models of rational economic agents, and are an invaluable supplement to any primary textbook in microeconomic theory. In this fully revised and expanded second edition, Rubinstein retains the striking originality and deep simplicity that characterize his famously engaging style of teaching. He presents these lecture notes with a precision that gets to the core of the material, and he places special emphasis on the interpretation of key concepts. Rubinstein brings this concise book thoroughly up to date, covering topics like modern choice theory and including dozens of original new problems. Written by one of the world's most respected and provocative economic theorists, this second edition of Lecture Notes in Microeconomic Theory is essential reading for students, teachers, and research economists. Fully revised, expanded, and updated Retains the engaging style and method of Rubinstein's well-known lectures Covers topics like modern choice theory Features numerous original new problems—including 21 new review problems Solutions manual (available only to teachers) can be found at: http://gametheory.tau.ac.il/microTheory/.
Download or read book An Introduction to the Economic Theory of Market Behavior written by Donald W. Katzner and published by Edward Elgar Publishing. This book was released on 2006-01-01 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This is an important, rigorous, and thoroughly engaging text on the economic theory of market behavior. It is unique in the attention devoted to the philosophical underpinnings and the historical background of the Walrasian Theory. Professor Katzner challenges his readers to understand the strengths and the limitations of what has gone before, and he provides guidance as to how he would like to see price theory develop in the future. This is among those rare texts that is designed to inspire further research.' - Hugo Sonnenschein, University of Chicago, US
Download or read book Models in Microeconomic Theory written by Martin J. Osborne and published by Open Book Publishers. This book was released on 2023-06-26 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models in Microeconomic Theory covers basic models in current microeconomic theory. Part I (Chapters 1-7) presents models of an economic agent, discussing abstract models of preferences, choice, and decision making under uncertainty, before turning to models of the consumer, the producer, and monopoly. Part II (Chapters 8-14) introduces the concept of equilibrium, beginning, unconventionally, with the models of the jungle and an economy with indivisible goods, and continuing with models of an exchange economy, equilibrium with rational expectations, and an economy with asymmetric information. Part III (Chapters 15-16) provides an introduction to game theory, covering strategic and extensive games and the concepts of Nash equilibrium and subgame perfect equilibrium. Part IV (Chapters 17-20) gives a taste of the topics of mechanism design, matching, the axiomatic analysis of economic systems, and social choice. The book focuses on the concepts of model and equilibrium. It states models and results precisely, and provides proofs for all results. It uses only elementary mathematics (with almost no calculus), although many of the proofs involve sustained logical arguments. It includes about 150 exercises. With its formal but accessible style, this textbook is designed for undergraduate students of microeconomics at intermediate and advanced levels.
Download or read book Double Hierarchy Linguistic Term Set and Its Extensions written by Xunjie Gou and published by Springer Nature. This book was released on 2020-06-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the concept of the double hierarchy linguistic term set and its extensions, which can deal with dynamic and complex decision-making problems. With the rapid development of science and technology and the acceleration of information updating, the complexity of decision-making problems has become increasingly obvious. This book provides a comprehensive and systematic introduction to the latest research in the field, including measurement methods, consistency methods, group consensus and large-scale group consensus decision-making methods, as well as their practical applications. Intended for engineers, technicians, and researchers in the fields of computer linguistics, operations research, information science, management science and engineering, it also serves as a textbook for postgraduate and senior undergraduate university students.
Download or read book The Journal of Agricultural Economics Research written by and published by . This book was released on 1994 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Representation of Preference Orders and the Construction of Utility Functions from Expenditures written by L.F. Lee and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Preferences Choice Mechanisms and Welfare written by Ludwig von Auer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most economic aspects of human behaviour, static deci sion models provide an insufficient description. More specifically, they ignore the fact that preferences may change over time and that at each point of time current preferences depend on aspects which are associated with the past or the future. The neglect of these phenomena may lead to results which have little in com mon with real life. Dynamic decision models were developed in order to cope with these complications. Spurred by the availability of new mathematical tools such as optimal control theory and dynamic programming, dynamic utility models mushroomed over the last two decades. Various frameworks were developed featuring dif ferent restrictions on the way agents form preferences in an in tertemporal environment. Unfortunately, no systematic reappraisal of this literature ex ists. The survey provided in part I of this thesis attempts to fill in this gap. It introduces a comprehensive classification sys tem which allows for a coherent organization of all studies of intertemporal choice under certainty and complete information. 2 1. Introduction The latter implies that the individual knows in advance all fu ture preferences and choice possibilities. In this survey we show that all dynamic utility models can be viewed as special cases of the class of universal utility mod els. It is therefore desirable to investigate intertemporal decision making in terms of this least restrictive framework. Accordingly, all findings of part II of this thesis are derived for the class of universal utility models.
