General equilibrium analysis is a theoretical structure which focuses research in economics. On this point economists and philosophers agree. Yet studies in general equilibrium analyses are not well understood in the sense that, though their importance is recognized, their role in the growth of economic knowledge is a subject of some controversy. Several questions organize an appraisal of general equilibrium analysis. These questions have been variously posed by philosophers of science, economic methodologists, and historians (...) of economic thought. Is general equilibrium analysis a theory, a paradigm, a scientific research program, or a set of interrelated theories? Is it not any of these but rather a branch of applied mathematics? Is GE analysis associated with the growth of knowledge, or does it waste intellectual resources? How is it related to other work in economics? Is it connected to, or is it apart from, the concerns of applied economists? (shrink)

What is the nature of the intellectual enterprise - general equilibrium analysis - that so many economists regard as the centerpiece of their discipline? In this book, Roy Weintraub considers both the modern history of the analysis, and the methodological puzzles that it, and mathematical economic theory in general, pose. Professor Weintraub argues that previous writings on the history and method of general equilibrium theory have been curiously biased and misleading. He provides a clear and (...) careful presentation of the development of the theory from the 1930s through to the Arrow-Debreu work of the 1950s. This historical analysis is the centre of the book: a case study which permits the author to justify the status of general equilibrium theory in economics and the activity in which economic theorists engage. He argues that previous methodological investigations have been distorted by their use of inappropriate models taken from the philosophy of science that were developed to appraise work in the physical sciences. (shrink)

Although general equilibrium theory originated in the late nineteenth century, modern elaboration and development of the theory began only in the 1930s and 1940s. This book focuses on the version of the theory developed in the second half of the twentieth century, referred to by Lionel McKenzie as the classical general equilibrium theory. McKenzie offers detailed and rigorous treatment of the classical model, giving step-by-step proofs of the basic theorems. In many cases he elaborates on the (...) individual steps to give a fuller understanding of the underlying principles. His goal is to provide readers with a true mastery of the methodology so that they can derive new results that will further enrich their thinking about general equilibrium theory. Special attention is given to the McKenzie model, in which it is not assumed that the number of firms is given but rather that technologies or activities are available to any agents who can supply the resources they require. The McKenzie model is used to establish the turnpike theorems of optimal and competitive capital accumulation. (shrink)

General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear (...) first as functions, then optionally as correspondences. The mathematics presented includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition. (shrink)

Most philosophers of economics are hostile towards neoclassical economics in general and general equilibrium theory in the vein of Arrow and Debreu in particular. Especially the latter’s dismissal is justified by pointing out its lack of direct relevance for an understanding of real economies. Many recommend a more pragmatic approach along the lines of Keynes instead. The criterion of scientific legitimacy underlying this approach derives from a philosophy of science developed along the lines of Popper and Lakatos. (...) They, however, neglect the importance of conceptual problems and of the choice of adequate ‘language-systems’ in science. Since these conceptual and ‘linguistic’ aspects may be able to explain and to justify the rationale of the Arrow-Debreu approach, I recommend the more balanced philosophies of Carnap and Laudan, in which conceptual as well as empirical problems are allowed for, as a framework for methodological appraisal. I explain why such a balanced view is obstructed for most philosophers of economics and advocate a moderate pluralism leaving room for different theories, methodologies and language-systems, depending on the scientific aims that are pursued. (shrink)

The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production.Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to (...) which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field. (shrink)

This book presents a collection of articles on applied general equilibrium analysis by major contributors to this field. This rapidly expanding method of analysis involves the use of computers to study entire economies and the interrelationships among firms, households and governments in these economies. There are also articles on the particular computational techniques involved in the numerical estimation of these equilibrium models and on several particular applications. Papers deal with the United States, Mexican and Australian economies. Other (...) chapters provide an analysis of long-run energy problems, fiscal federalism and economic planning. (shrink)

The aim of this book is to make more widely available a body of recent research activity that has become known as applied general equilibrium analysis. The central idea underlying this work is to convert the Walrasian general equilibrium structure from an abstract representation of an economy into realistic models of actual economies. Numerical, empirically based general equilibrium models can then be used to evaluate concrete policy options by specifying production and demand parameters and (...) incorporating data reflective of real economies. Shoven and Whalley describe all aspects of developing applied general equilibrium models, including developing an appropriate equilibrium structure, calibrating the model, compiling counterfactual equilibria, and interpreting results. The authors contend that the Walrasian general equilibrium model provides an ideal framework for appraising the effects of policy changes on resource allocation, assessing who gains and who loses, and the policy impacts not well covered by empirical macro models. The applications in the book illustrate a number of ways in which fresh insights are provided in longstanding policy controversies. (shrink)

This book, together with Marx's Economic and Walras' Economics, completes a sequence of titles by Professor Morishima on the first generation of scientific economists. The author's assessment of Ricardo differs substantially from the established views adopted by economists and historians of economic thought. While economists such as Pasinetti, Caravale and Samuelson have concentrated on macroeconomic interpretations of Ricardo, and historians of economic thought have emphasised his labour theory of value, Morishima takes a different course. In this book the author concentrates (...) on Ricardo's main work, The Principles, and shows that his economics is the prototype of mathematical economies without the symbols and formulae. Morishima then translates Ricardo's economics into mathematical language to find a general equilibrium system concealed within. The analysis also contradicts the conventional view that marginalism emerged in opposition to classical economics, showing instead that Ricardian analysis is firmly based on marginalist principles, using prices, wages and profits rather than labour values. The book ends with a discussion of the historical character of economic theory and an attempt to specify the epoch of Ricardian economics. (shrink)

Computable general equilibrium models are widely used by governmental organizations and academic institutions to analyze the economy-wide effects of events such as climate change, tax policies and immigration. This book provides a practical, how-to guide to CGE models suitable for use at the undergraduate college level. Its introductory level distinguishes it from other available books and articles on CGE models. The book provides intuitive and graphical explanations of the economic theory that underlies a CGE model and includes many (...) examples and hands-on modeling exercises. It may be used in courses on economics principles, microeconomics, macroeconomics, public finance, environmental economics and international trade and finance, because it shows students the role of theory in a realistic model of an economy. The book is also suitable for courses on general equilibrium models and research methods and for professionals interested in learning how to use CGE models. (shrink)

Applied general equilibrium models have received considerable attention and scrutiny in the public debate over the North American Free Trade Agreement. This collection brings together the leading AGE models that have been constructed to analyse NAFTA. A variety of approaches to modelling trade liberalization are taken in these studies, including multi-country and multi-sectoral models, models that focus on institutional features of particular sectors affecting multinational firms and rules of origin, and models with some inter-temporal structure. Further, by constructing (...) stylized models, theoretical linkages have been identified that drive numerical results in the larger AGE models. The volume also assesses what can be learned about the likely economic effects of NAFTA from the collection of studies taken as a whole. Areas in need of further study have been highlighted. (shrink)

This 2005 volume brings together twelve papers by many of the most prominent applied general equilibrium modelers honoring Herbert Scarf, the father of equilibrium computation in economics. It deals with developments in applied general equilibrium, a field which has broadened greatly since the 1980s. The contributors discuss some traditional as well as some modern topics in the field, including non-convexities in economy-wide models, tax policy, developmental modeling and energy modeling. The book also covers a range (...) of distinct approaches, conceptual issues and computational algorithms, such as calibration and areas of application such as macroeconomics of real business cycles and finance. An introductory chapter written by the editors maps out issues and scenarios for the future evolution of applied general equilibrium. (shrink)

First published in 1985 and written by leading contributors to the field of general equilibrium analysis, this volume brings together developments in the field of applied general equilibrium modelling. Papers discuss approaches to welfare measurement in applied models, applications to hitherto unexplored areas, such as economic history, extensions to analyse micro data files, regional analyses, fixed price equilibria, and many others. Earlier versions of the papers in this volume were presented at a conference held in Canberra, (...) Australia. (shrink)

The theory of competition has held a central place in economic analysis since Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of perfect competition. Beginning with a concise survey of how the theory of competition has evolved, Gale makes extensive and rigorous use of dynamic matching and bargaining models to provide a more complete description of how a competitive equlibrium is (...) achieved. Whereas economists have made use of a macroscopic description of markets in which certain behavioral characteristics, such as price-taking behavior, are taken for granted, Gale uses game theory to re-evaluate this assumption, beginning with individual agents and modelling their strategic interaction. A strategic foundation for competitive equilibrium shows how such interaction leads to competitive, price-taking behavior. Essential reading for graduate courses in game theory and general equilibrium. (shrink)

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical (...) how-possibly explanation which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding. (shrink)

Economic methodologists most often study the relations between models and reality while focusing on the issues of the model's epistemic relevance in terms of its relation to the ‘real world’ and representing the real world in a model. We complement the discussion by bringing the model's constructive mechanisms or self-implementing technologies in play. By this, we mean the elements of the economic model that are aimed at ‘implementing’ it by envisaging the ways to change the reality in order to bring (...) it more in line with the model. We are thus concerned mainly not with the ways to change the model to ‘fit’ the reality, but rather with the model's own armature that is supposed to transform the world along theoretical lines. The case we study is Arrow–Debreu–McKenzie general equilibrium model. In particular, we show the following: gradient methods and stability could be regarded as constructive mechanisms of general equilibrium modeling in the context of market socialism debates; the obsession of general eq.. (shrink)

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of (...) philosophers who have offered a general epistemic justification of such practices. (shrink)

Contemporary general equilibrium theory is characteristically short-run, separated from monetary aspects of the economy, and as such does not deal with long-run problems such as capital accumulation, innovation, and the historical movement of the economy. These phenomena are discussed by growth theory, which assumes a given or shifting production function, and in turn cannot therefore deal with the fundamental problem of growth, namely how the production function is derived. Thus traditional theories have a common weakness in that they (...) divorce real economic growth from the activities of the financial sector. This book provides a much-needed synthesis of growth theory and monetary theory. Professor Morishima draws on the work of Schumpeter, Keynes and the pre-war neoclassical economists to formulate a capital-theoretic general equilibrium theory. (shrink)

This paper provides an in-depth study and analysis of the quantitative relationship between ASEAN industry transfer and nuclear trade restructuring through the multiregional computable general equilibrium model and categorizes the ten major projects and 57 subprojects covered by the ASEAN Information Port project investment into construction, information technology, and telecommunications, according to the key directions of investment. We design and simulate the changes in production activities, trade activities, and the balance of payments behaviour of the national economy affected (...) by the project’s investment under 10 types of investment amount scenarios and prepare the corresponding social accounting matrix. Increased trade openness increases external risks and instability of the economy and fiscal revenues. At the same time, it creates other potential problems for the country such as environmental pollution and leading to unfair competition. Under free trade conditions, some manufacturers may choose to produce inputs that are not environmentally friendly to reduce costs, thereby harming the environment. For infant industries, if the government does not provide them with short-term protection or supportive policies, these new or developing infant industries may not have strong international competitiveness and may be vulnerable to the attacks of mature industries in the world. Therefore, based on the study of the influence of tax policy on trade openness, this paper examines the impact of changes in trade openness on a country’s economic environment and takes tax revenue as an example to conduct an empirical analysis and improve the factors that need to be considered when adjusting tax policy. (shrink)

This paper considers in detail the ontological and normative presuppositions of the state-contingent approach to pricing commodities first introduced by Arrow in his model of general equilibrium under uncertainty, which became a milestone in the theory of finance. By contextualizing Arrow’s fundamental contribution and subsequent developments in finance, it demonstrates how this new conceptual framework implied certain technologies—both intellectual and financial. In showing how theoretical thinking about finance was underlying institutional developments in finance, this paper complements the familiar (...) narrative of the performativity of economics. (shrink)

Bruce Caldwell has disputed a number of points in my earlier account of the development of the Austrian school of economics from Carl Menger to Ludwig von Mises and F.A. Hayek. The issues in contention regard Friedrich von Wieser’s intellectual affiliation with Hayek and his influence on the formation of Hayek’s economic thought; Wieser’s status as a general equilibrium theorist; and the reason for Hayek’s early flirtation with general equilibrium theory. In this article I argue that (...) Hayek was a self-conscious adherent of the Wieserian tradition and remained so even after he received the Nobel Prize in 1974 and that he distinguished between this tradition and the Böhm-Bawerkian tradition followed by Ludwig von Mises. I also contend that Wieser used the construction of a general equilibrium economy subject to a single will as both a normative benchmark by which to appraise the performance of the real-world market economy and as an analytical tool to explain the formation of market prices. Finally, I argue that Hayek concerned himself with the problems of the Wieser-type general equilibrium economy beginning with his earliest writings as a professional economist, years before he began to focus on the theoretical problems of money and the business cycle.Bruce Caldwell a discuté un certain nombre de points de mon article récent sur le développement de l’école autrichienne d’économie de Carl Menger en passant par Ludwig von Mises et F.A. Hayek. Les controverses concernant l’affiliation intellectuelle de Hayek vis-à-vis de Friedrich von Wieser et l’influence de ce dernier sur la pensée économique de Hayek, le statut de Wieser en tant que théoricien de l’équilibre général, et les raisons pour lesquelles le jeune Hayek flirta avec la théorie de l’équilibre général.Dans cet article je défends la thèse selon laquelle Hayek était conscient du fait qu’il s’inscrivait dans la tradition Wieserienne et qu’il l’était toujours même après sa réception du prix Nobel en 1974 et quand il fît la distinction entre cette tradition et la tradition inaugurée par Böhm-Bawerk et poursuivie par Mises. L’article affirme aussi que Wieser utilisa la construction d’une économie en équilibre général sujette à une volonté unique à la fois comme standard normatif pour évaluer les performances des marchés dans le monde réel et comme outil analytique pour expliquer la formation des prix marchands. Enfin, l’article argumente que Hayek s’intéressa aux problèmes relevant d’une économie en équilibre général à la Wieser dans ses premiers écrits en tant qu’économiste et cela bien avant qu’il ne se concentrât sur les problèmes théoriques de la monnaie et du cycle des affaires. (shrink)

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments (...) in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis. (shrink)

In this note we argue that Lars von Trier’s movie Dogville can be viewed as an illustration of a simple economy where one agent has only her body as initial endowment. The movie illustrates some interesting comparative statics of equilibrium allocations. It shows how life would be like in a world where, in the absence of constitutional or legal constraints, economic forces reign freely and raises some fundamental issues of voluntary exchange versus force that apply to a number of (...) contentious issues in public debate. JEL codes: A20, D30, D51, D63, F13. Keywords: Dogville, general equilibrium, welfare theorems, comparative statics, international trade, child labor, prostitution, economics education. (shrink)

The resurgence of rational choice theory in sociology has given rise to a debate about its scope and limits. This paper approaches the debate in a constructive spirit. Taking Coleman's recent work as exemplary of rational choice theory in sociology, the discussion begins by noticing some elements common to this theory and to the framework employed by neofunctionalist critics of rational choice theory. First, the concept of control plays a central role in both theoretical models. Second, both theories attempt to (...) generalize the general equilibrium theory of economics, thereby capturing the economic theory as a special case. The constructive work consists of showing how key concepts of one model relate to analogous key concepts in the other. The aim is to forge the beginning of the synthesis in which the strengths of each model are preserved in one that includes both. (shrink)

The book is very well structured to support practical skills development in understanding DSGE modelling through exercises to graduate a user knowledge on macroeconomic application relevant for policy decisions through use of scientific programs like DYNARE /IRIS, appropriate for use with MatLab/Octave. The author also provided useful references for the more inquisitive reader or practitioner to develop his / her ontological quest for further knowledge in the macroeconomic management of a state (Jackson, 2016). On the basis of relevance of its (...) contents pertaining to theoretical application of macroeconomic policy and management of an economy, I strongly recommend this book to anyone preparing for graduate courses in Economics and related areas like Econometrics, Economic Policy Management and also, to the practitioner-researcher engaged in macroeconomic model construction and policy formulation. (shrink)

In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of (...) differentiability assumptions and the application of the methods of differential topology to the study of the equilibrium equation. Balasko's rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium's evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern" developments of the Arrow-Debreu model improve our understanding of modern market economies. (shrink)

Andreu Mas-Colell has been doing pioneering work using differential topology in the analysis of general equilibrium. This work is regarded as outstanding and one of the major contributions to the development of rigorous economic theory in the last twenty years. The articles he has written have been difficult and technically demanding. In this book he brings this work together to show its scope and its power. He presents the analysis in a way which makes it accessible to the (...) broader range of economic theorists and advanced students. This book has been long awaited as a seminal contribution to the subject. (shrink)

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an (...) existence theorem which provides general criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)

The method of reflective equilibrium focuses on the relationship between principles and judgments. Principles are relatively general rules for comprehending the area of enquiry. Judgments are our intuitions or commitments, ‘at all levels of generality’ (Rawls 1975: 8), regarding the subject matter. The basic idea of reflective equilibrium is to bring principles and judgments into accord. This can be achieved by revising the principles and/or the judgments. -/- I first look at normative political judgments (Section 2) before (...) considering the role of principles, arguments, devices of representation and background theory in wide reflective equilibrium (Section 3). I then consider two of the main challenges to the method (Section 4), and show how to use it to deliberate about substantive political principles (Section 5). I conclude with an extended example of the method in action (Section 6). (shrink)

The development of general equilibrium theory represents one of the greatest advances in economic analysis in the latter half of the twentieth century. This book, intended for advanced undergraduates and graduate students, provides a broad introduction to competitive equilibrium analysis with an emphasis on concrete applications. The first three chapters are introductory in nature, paving the way for the more advanced second half of the book. Relative to the competition, it is much more 'user friendly' while offering (...) exceptionally broad coverage of topics. Well-designed and interesting applications help to make potentially abstract material more accessible. The book includes 92 illustrations and nearly 200 exercises. (shrink)

Recent years have seen a rekindling of interest in the method of reflective equilibrium. Most of this attention has been suspicious, however. Critics have alleged that the method is nothing more than a high-minded brand of navel-gazing, that it suffers from all the classic problems of inward-looking coherence theories, and that it overestimates the usefulness of self-scrutiny. In this paper I argue that these criticisms miss their mark because they labor under crucial misconceptions about the method of reflective (...) class='Hi'>equilibrium. In defending reflective equilibrium I put forward a handful of theses about the nature of inquiry (or, more generally, norm-governed enterprises) that form the backdrop to the method. The critics’ objections fall short, I argue, because they do not recognize reflective equilibrium’s embrace of these theses. Confronting these objections and understanding why they fail brings us to a better understanding what, exactly, the method of reflective equilibrium is. The answer I come to in the final section of the paper is that the method of reflective equilibrium is not, exactly, anything. It is a mistake to try to give a positive characterization of the view, to identify it with a concern with a particular species of data, particular procedures and methods, or even a particular conception of normative success. Instead, it should be understood as the denial of essentialism about just these matters—as a form of anti-essentialism about our epistemic inputs, methods, and goals. (shrink)

According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly (...) any attention. Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (shrink)

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible (...) to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)

How can we figure out what’s right or wrong, if moral truths are neither self-evident nor something we can perceive? Very roughly, the method of reflective equilibrium (RE) says that we should begin moral inquiry from what we already confidently think, seeking to find a a match between our initial convictions and general principles that are well-supported by background theories, mutually adjusting both until we reach a coherent outlook in which our beliefs are in harmony (the equilibrium (...) part) and we know why and how they support each other (the reflective part). It has been central to the self-understanding of normative ethics and other branches of philosophy in the last half a century. In this chapter, we examine the history of the idea of RE and introduce a schema for generating 256 variants. We explain why RE is subject to serious objections insofar as it purports to yield epistemic justification in virtue of achieving coherence. However, we also develop a new argument to the effect that RE is the best feasible method for us to achieve moral understanding and the ability to justify our judgments to others. It may thus be crucial for responsible moral inquiry, even if coherence among considered judgments and principles is neither sufficient nor necessary for justified moral belief. (shrink)

Equilibrium explanations use an equilibrium to represent and explain a system’s dynamic behavior. They provide a system with the property of global stability: a system will converge towards and remain in equilibrium regardless of its initial conditions and dynamic process. Thus, equilibrium explanations are generally treated as non-causal explanations. There are two claims subsumed under that comprehensive thesis. The first claim is that equilibrium explanations do not identify any causes because a system with global stability (...) resists manipulation. The second claim is that even if equilibrium explanations do identify causes by manipulation, those causes are embedded in a system’s deeper, underlying structural relationships, and those causes are irrelevant to explaining a system’s behavior. Only the system’s structural relationships are relevant. But equilibrium explanations are not monolithic. I compare dynamic systems with multiple, competing equilibria to systems with a globally stable equilibrium. Equilibrium explanations of the former use intervention on a system’s initial conditions and dynamic process to manipulate equilibria, which identifies causes. Furthermore, a system’s initial conditions and dynamic process are relevant to explaining why one equilibrium is selected instead of another. I then apply these lessons to systems with a globally stable equilibrium and discuss when their corresponding equilibrium explanations have a proper role in the parent sciences. (shrink)

As a procedure, reflective equilibrium is simply a familiar kind of standard scientific method with a new name. A theory is constructed to account for a set of observations. Recalcitrant data may be rejected as noise or explained away as the effects of interference of some sort. Recalcitrant data that cannot be plausibly dismissed force emendations in theory. What counts as a plausible dismissal depends, among other things, on the going theory, as well as on background theory and on (...) knowledge that may be relevant to under-standing the experimental design that is generating the observations, including knowledge of the apparatus and observation conditions. This sort of mutual adjustment between theory and data is a familiar feature of scientific practice. Whatever authority RE seems to have comes, I think, from a tacit or explicit recognition that it has the same form as this familiar sort of scientific inference. One way to see the rationale underlying this procedure in science is to focus on prediction. Think of prediction as a matter of projecting what is known onto uncharted territory. To do this, you need a vehicle—a theory—that captures some invariant or pattern in what is known so that you can project it onto the unknown. How convincing the projection is depends on two factors: how sure one is of the observational base, and how sure one is that the theory gets the invariants right. The two factors are not independent, of course. One's confidence in the observational base will be affected by how persuasively the theory identifies and dismisses noise; one's confidence in the theory, on the other hand, will depend on one's confidence in the observations it takes seriously. Prediction is important as a test of theory precisely because verified predictions seem to show that the theory has correctly captured the general in the particular, that it has got the drift of the observational evidence in which our confidence is ultimately grounded. (shrink)

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in (...) full generality -- i.e. without making any assumptions about the system's dynamics or the nature of the interactions between its components -- that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another -- again fully general -- theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor, the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem. (shrink)

Practical equilibrium, like reflective equilibrium, is a way of deciding what to think about morality. It shares with reflective equilibrium the general thesis that there is some way in which a moral theory must, in order to be acceptable, answer to one’s moral intuitions, but it differs from reflective equilibrium in its specification of exactly how a moral theory must answer to one’s intuitions. Whereas reflective equilibrium focuses on a theory’s consistency with those intuitions, (...) practical equilibrium also gives weight to a theory’s approval of one’s having those intuitions. (shrink)