Non Archimedean Utility Theory
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Non Archimedean Utility Theory
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Author : Heinz J. Skala
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Archimedean Utility Theory written by Heinz J. Skala and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
My interest in non-Archimedean utility theory and the problems related to it was aroused by discussions which I have had with Professors Werner Leinfellner and Günter Menges. On the occasion of the Second Inter national Game Theory Workshop, Berkeley, 1970, which was sponsored by the National Science Foundation, I had the opportunity to report about a result on non-standard utilities. Work on this subject continued when I was a research assistant of Professor Günter Menges at the Uni versity of Heidelberg. The present mono graph is essentially a translation of my habilitation thesis which was accepted on February 15, 1973 by the Faculty of Economics and Social Sciences at the Universtity of Heidelberg. On translating my thesis I took up some suggestions made by ProfessorWerner Böge from the Faculty of Mathematics at the Uni versity of Heidelberg. Through lack of time many of his ideas have not been taken into consideration but I hope to do so in a future paper. The first chapter should be considered as a short introduction to pref erence orderings and to the notion of a utility theory proposed by Dana Scott and Patrick Suppes. In the second chapter I discuss in some detail various problems of ordinal utility theory. Except when introducing non-standard models of the reals no use is made of concepts of model theory. This is done in deference to those readers who do not wish to be troubled by formal languages and model theory.
Axiomatic Utility Theory Under Risk
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Author : Ulrich Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Axiomatic Utility Theory Under Risk written by Ulrich Schmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
The first attempts to develop a utility theory for choice situations under risk were undertaken by Cramer (1728) and Bernoulli (1738). Considering the famous St. Petersburg Paradox! - a lottery with an infinite expected monetary value -Bernoulli (1738, p. 209) observed that most people would not spend a significant amount of money to engage in that gamble. To account for this observation, Bernoulli (1738, pp. 199-201) proposed that the expected monetary value has to be replaced by the expected utility ("moral expectation") as the relevant criterion for decision making under risk. However, Bernoulli's 2 argument and particularly his choice of a logarithmic utility function seem to be rather arbitrary since they are based entirely on intuitively 3 appealing examples. Not until two centuries later, did von Neumann and Morgenstern (1947) prove that if the preferences of the decision maker satisfy cer tain assumptions they can be represented by the expected value of a real-valued utility function defined on the set of consequences. Despite the identical mathematical form of expected utility, the theory of von Neumann and Morgenstern and Bernoulli's approach have, however, IFor comprehensive discussions of this paradox cf. Menger (1934), Samuelson (1960), (1977), Shapley (1977a), Aumann (1977), Jorland (1987), and Zabell (1987). 2Cramer (1728, p. 212), on the other hand, proposed that the utility of an amount of money is given by the square root of this amount.
Advances In Non Archimedean Analysis And Applications
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Author : W. A. Zúñiga-Galindo
language : en
Publisher: Springer Nature
Release Date : 2021-12-02
Advances In Non Archimedean Analysis And Applications written by W. A. Zúñiga-Galindo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Mathematics categories.
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role – a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems – for instance, proteins – asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
Utility Theories Measurements And Applications
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Author : Ward Edwards
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Utility Theories Measurements And Applications written by Ward Edwards and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Business & Economics categories.
The Conference on "Utility: Theories, Measurements, and Applications" met at the Inn at Pasatiempo in Santa Cruz, California, from June II to 15, 1989. The all-star cast of attendees are listed as authors in the Table of Contents of this book (see p. V), except for Soo Hong Chew and Amos Tversky. The purpose of the conference, and of National Science Foundation Grant No. SES-8823012 that supported it, was to confront proponents of new generalized theories of utility with leading decision analysts com mitted to the implementation, in practice, of the more traditional theory that these new theories reject. That traditional model is variously iden tified in this book as expected utility or subjectively expected utility maximization (EU or SEU for short) and variously attributed to von Neumann and Morgenstern or Savage. I had feared that the conference might consist of an acrimonious debate between Olympian normative theorists uninterested in what people actually do and behavioral modelers obsessed with the cognitive illusions and uninterested in helping people to make wise decisions. I was entirely wrong. The conferees, in two dramatic straw votes at the open ing session, unanimously endorsed traditional SEU as the appropriate normative model and unanimously agreed that people don't act as that model requires. (These votes had a profound impact on my thinking; detail about them and about that impact is located in Chapter 10.
Non Archimedean Subjective Probabilities In Decision Theory And Games
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Author : Peter J. Hammond
language : en
Publisher:
Release Date : 1998
Non Archimedean Subjective Probabilities In Decision Theory And Games written by Peter J. Hammond and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963) and in Blume, Brandenburger and Dekel (1991) are used to characterize preferences which: (i) reveal unique non-Archimedean subjective probabilities within the field; and (ii) can be represented by the non-Archimedean subjective expected value of any real-valued von Neumann-Morgenstern utility function in a unique cardinal equivalence class, using the natural ordering of the field.
The Foundations Of Expected Utility
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Author : P.C. Fishburn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Foundations Of Expected Utility written by P.C. Fishburn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Social Science categories.
This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under uncertainty. Both parts are studies in the axiomatics of preferences for decision situations and in numerical representations for preferences. Proofs of the representation and uniqueness theorems appear at the ends of the chapters so as not to impede the flow of the discussion. A few warnings on notation are in order. The numbers for theorems cited within a chapter have no prefix if they appear in that chapter, but otherwise carry a chapter prefix (Theorem 3.2 is Theorem 2 in Chapter 3). All lower case Greek letters refer to numbers in the closed interval from o to 1. The same symbol in different chapters has essentially the same meaning with one major exception: x, y, ... mean quite different things in different chapters. I am indebted to many people for their help and encouragement.
Patrick Suppes Scientific Philosopher
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Author : P. Humphreys
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Patrick Suppes Scientific Philosopher written by P. Humphreys and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Patrick Suppes is a philosopher and scientist whose contributions range over probability and statistics, mathematical and experimental psychology, the foundations of physics, education theory, the philosophy of language, measurement theory, and the philosophy of science. He has also been a pioneer in the area of computer assisted instruction. In each of these areas, Suppes has provided seminal ideas that in some cases led to shaping the direction of research in the field. The papers contained in this collection were commissioned with the mandate of advancing research in their respective fields rather than retrospectively surveying the contributions that Suppes himself has made. The authors form an interesting mixture of researchers in both formal philosophy of science and science itself all of whom have been inspired by his ideas. To maintain the spirit of constructive dialogue that characterizes Suppes's intellectual style, he has written individual responses to each article. In Volume 1: Probability and Probabilistic Causality, nineteen distinguished philosophers and scientists focus their attention on probabilistic issues. In Part I the contributors explore axiomatic representations of probability theory including qualitative and interval valued probabilities as well as traditional point valued probabilities. Belief structures and the dynamics of belief are also treated in detail. In Part II the rapidly growing field of probabilistic causation is assessed from both formal and empirical viewpoints. For probability theorists, statisticians, economists, philosophers of science, psychologists and those interested in the foundations of mathematical social science. In Volume 2: Philosophy of Physics, Theory Structure, and Measurement Theory, fifteen distinguished philosophers and scientists cover a wide variety of topics. Part III covers issues in quantum theory, geometry, classical mechanics, and computational physics. Part IV explores Suppes's well known set-theoretic account of scientific theories which has served him well throughout his career. Suppes's contributions to measurement theory have been widely used in mathematical psychology and elsewhere, and this material is the subject of Part V. For physicists, logicians, workers in mathematical social sicence, and philosophers of science. In Volume 3: Philosophy of Language and Logic, Learning and Action Theory, fourteen distinguished philosophers and scientists explore issues in the philosophy of language, logic, and philosophical psychology. Suppes's suggestions that quantum theory requires a rethinking of classical logic form a particularly sharp account of that controversial thesis, and Part VI deals with this issue together with topics in the philosophy of language and logic, including relational grammars and anaphora. Part VII deals with issues in psychology, action theory, and robotics, while Part VIII concludes with a general survey of Suppes's views in the philosophy of science. A comprehensive chronological and topical bibliography of Suppes's writings is included in this volume. For philosophers of language, theoretical linguists, logicians, workers in mathematical social sciences, and philosophers of science.
A Theory Of Social Action
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Author : R. Tuomela
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Theory Of Social Action written by R. Tuomela and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
It is somewhat surprising to find out how little serious theorizing there is in philosophy (and in social psychology as well as sociology) on the nature of social actions or joint act. hons in the sense of actions performed together by several agents. Actions performed by single agents have been extensively discussed both in philosophy and in psycho~ogy. There is, ac cordingly, a booming field called action theory in philosophy but it has so far strongly concentrated on actions performed by single agents only. We of course should not forget game theory, a discipline that systematically studies the strategic interac tion between several rational agents. Yet this important theory, besides being restricted to strongly rational acting, fails to study properly several central problems related to the concep tual nature of social action. Thus, it does not adequately clarify and classify the various types of joint action (except perhaps from the point of view of the agents' utilities). This book presents a systematic theory of social action. Because of its reliance on so-called purposive causation and generation it is called the purposive-causal theory. This work also discusses several problems related to the topic of social action, for instance that of how to create from this perspective the most central concepts needed by social psychology and soci ology. While quite a lot of ground is covered in the book, many important questions have been left unanswered and many others unasked as well.
When No Price Is Right
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Author : Mark Schervish
language : en
Publisher:
Release Date : 2022
When No Price Is Right written by Mark Schervish and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by anonstandard utility function. Non-Archimedean preferences arise when somerandom quantities have no fair price. Two common situations give riseto non-Archimedean preferences: random quantities whose values must be greater than every real number, and strict preferences betweenrandom quantities that are deemed closer in value thanevery positive real number. We also show how to extend anon-Archimedean preference to a larger set of random quantities. Therandom quantities that we consider include real-valued randomvariables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions madeby the existing theories and give conditions under which the utilitythat represents preference is the expected value of a state-dependentutility with respect to a probability over states.
Pascal S Wager
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Author : Paul Bartha
language : en
Publisher: Cambridge University Press
Release Date : 2018-10-18
Pascal S Wager written by Paul Bartha and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Philosophy categories.
Presents a comprehensive examination of Pascal's Wager, its underlying theology, philosophical influence, and role in contemporary decision theory.