This paper suggests that Nash equilibrium can be interpreted as a conceptual tool for addressing comparative-statics issues on an aggregate level. Together with additional assumptions, Nash equilibrium helps generate testable predictions about changes or differences of behavior induced by changes or differences of exogenous variables. However, Nash-equilibrium behavior, as such, is not subject to empirical testing. Instead, widespread and persistent behavior is modeled as a Nash equilibrium by assumption. The paper argues that this interpretation is in (...) line with the traditional use of an equilibrium concept in price theory. The suggested interpretation is illustrated with the model of public-goods provision. The paper compares this interpretation of Nash equilibrium with other interpretations and discusses its limits. (shrink)

One of the fundamental themes in economic theory is the study of the role of prices in achieving an optimal allocation of resources in a competitive, decentralized economy. The book begins with a review of the basic results on the rigorous elaboration of the Walras-Pareto theory in the context of a static economy with many agents. It summarizes some subsequent research in which the limits of the price-mechanism as a successful coordination device are recognized. When economic activity is allowed (...) with no pre-assigned terminal period, the two fundamental theorems linking competitive equilibrium allocations to Pareto optimality are challenged and the question of decentralization is carefully re-examined. With incomplete markets, and sequential trading, the concept of a Radner equilibrium is next introduced, and some of the striking properties of this are summarized. In a large economy with random shocks to preferences and/or endowments of individual agents, the implications of the celebrated laws of probability theory are explored. This book provides a clear and comprehensive analysis of the efficiency properties of general equilibrium, with many agents and an expanded list of commodities. It will be of particular interest to postgraduate and doctorate students of economic theory as well as scholars on Walrasian equilibrium, Pareto optimality and uncertainty theories. (shrink)

Social scientists, political scientists and philosophers debate key concepts such as democracy, power and autonomy. Contested concepts like these pose questions: Are terms such as “democracy” hopelessly ambiguous? How can two theorists defend alternative accounts of democracy without talking past each other? How can we understand debates in which theorists disagree about what democracy is? This paper first discusses the popular strategy to answer these questions by appealing to Rawls’s distinction between concepts and conceptions. According to this approach, defenders of (...) rival conceptions of, e.g. justice can disagree without talking past each other because they share the concept of justice. It is argued that this idea is attractive but limited in application and that it fails to do justice to the dynamic and normative aspects of concept formation. Reflective equilibrium is then suggested as an alternative approach. It replaces the static contrast between a conceptual ‘core’ and competing conceptions by a dynamic perspective of concept formation as a partly normative undertaking: pre-theoretic language use and commitments can provide a shared starting point for developing alternative accounts which yield different concepts of, e.g. justice. This perspective provides a new understanding of how it is possible that different theorists defend rival accounts of, e.g. justice, without talking past each other. (shrink)

This highly original book develops a systematic zero-net-profit comparative statics theory of the firm that challenges many widely held views in microeconomics. It builds a bridge between the marginalist long-run theory of the firm and Sraffian theory to create a unified theoretical framework that explains how firms react to exogenous shocks resulting in new equilibrium positions of the whole economy. The central message of the book is that too often economists expect more from the microeconomic laws of input demand (...) and output supply than they can really give. The authors show that the zero-net-profit condition requires a more articulated analysis that sometimes yields qualitative results contrary to those of familiar economic laws. Written for academic researchers and graduate students, the book will be of particular interest to those working on the microeconomics of industry equilibrium, comparative statics and Sraffian economics. (shrink)

Robert Lucas' article on the neutrality of money represented the first effective challenge to Samuelson’s neoclassical synthesis methodological separation between static microeconom...

This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement, called the Golden Rule of ethics (GR). This rule states, "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. The book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based (...) on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book of the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: a) a modification of N.N. Krasovskii's mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; b) the method of guiding control, proposed by N.N. Krasovskii; c) the Germeier convolution of the payoff functions of different players. Additionally, the book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2-4. The book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications. (shrink)

Game theory is often used to explain behavior. Such explanations often proceed by demonstrating that the behavior in question is a Nash equilibrium. Agents are in Nash equilibrium if each agent’s strategy maximizes her payoff given her opponents’ strategies. Nash equilibriums are fundamentally static, but it is usually assumed that equilibriums will be the outcome of a dynamic process of learning or evolution. This article demonstrates that, even in the most simple setting, this need not be true. (...) In two-strategy games with just a single equilibrium, a family of imitative learning dynamics does not lead to equilibrium. (shrink)

This dissertation attempts to settle some challenging historiographic issues concerning the origin and development of the concept of economic equilibrium. Specifically, our research goal is to identify the philosophical and historical drivers of the mathematization of economic theory. To this end, we attempt to answer three fundamental research questions. First, why (and not how) has economics become a mathematical science? Second, what are the major methodological blunders that lie at the foundations of Modern General Equilibrium Theory? Third, is (...) the contemporary criticism of Modern General Equilibrium Theory meaningful and well-founded? In order, chapters 1-3 address the first question, chapters 4 and 5 address the second, whereas chapter 6 addresses the third question. Regarding the first question, we investigate the methodological relationships between Modern Physics, Modern Philosophy, and Walras’s Theory of General Equilibrium. Interestingly, our findings reveal that while the study of motion in Modern Physics relies upon a clear distinction between static and dynamic equilibrium, early mathematical economics borrows its methodology from Modern Physics but relies upon an Aristotelian conception of equilibrium. Furthermore, we identify exciting analogies between Kant’s philosophy and Walras’s Elements. Finally, we show that the so-called Walras Paradox also features another unexplored dimension. Namely, Walras’s work overall relies upon a bottom-up approach to mathematics. Yet Walras’s work includes problems that require a top-down approach to mathematics to be solved. Regarding the second question, we delve into the tight relationship between the History of Mathematics in the 19th Century, the Philosophy of Mathematics in the 20th Century, and the development of Modern General Equilibrium Theory in the 20th Century. Notably, we find that the top-down approach to mathematics provides economists with a reliable methodology to resolve the problems in Walras’s original work. Hence, the mathematization of General Equilibrium Theory in the 20th Century is a child of its time that carries the inapplicability of pure mathematics to real-world problems along with itself. Therefore, although the mathematization of General Equilibrium Theory is an unprecedented milestone in economic theory, the foundations of Modern General Equilibrium Theory inherit the methodological shortcomings of Contemporary Mathematics. That is why the Sonnenschein-Mantel-Debreu does not overtake the Aristotelian conception of equilibrium. Accordingly, we rebut the claim that Debreu and colleagues' mathematization of General Equilibrium Theory resolves the fundamental methodological shortcomings of Walras’s original work. Eventually, we use our answers to our first and second research questions to address the contemporary criticism of General Equilibrium Theory. On the one hand, we show that the latter criticism does not account for the fact that General Equilibrium Theory inherits the scientific realism and determinism of Modern Physics. In other words, we argue that the inability of General Equilibrium models to manage uncertainty effectively has nothing to do with its mathematization in the 20th Century. Instead, it results from the unexplored dimension of the Walras Paradox, which we uncover. On the other hand, we show that common accusations of inconsistency, incompleteness, and undecidability in General Equilibrium Theory are ill-founded. That is because other rigorous alternatives to axiomatization in economics are not paradox-free. On these grounds, we conclude that a much better option is to employ a topic-neutral language to provide rigorous presentations of contested concepts in economics. Particularly, we show that formal mereology offers a convenient methodological framework to resolve the disagreement between the Neoclassical and Institutionalist economists’ respective definitions of the concept of the market. In this way, we show that the latter concept is definable as a process. But, more importantly, we note that formal mereology also offers a convenient framework to reformulate other economic concepts concisely and rigorously. In this regard, we observe that formal mereology might provide a resolution for Hayek’s Problem because it would enable economists to define general equilibrium as a perduring socioeconomic process. -/- In case you want a copy of my dissertation, please email me. (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 scientific world is, as I have often repeated, a shadow world, shadowing a world familiar to our consciousness. Just how much do we expect it to shadow? We do not expect it to shadow all that is in our mind, emotions, memory, etc. In the main we expect it to shadow impressions which can be traced to external sense organs. But time makes a dual entry and thus forms an intermediate link between the internal and the external. This is (...) shadowed partially by the scientific world of primary physics (which excludes time's arrow), but fully when we enlarge the scheme to include entropy. Therefore by the momentous departure in the nineteenth century the scientific world is not confined to a static extension around which the mind may spin a romance of activity and evolution; it shadows that dynamic quality of the familiar world which cannot be parted from it without disaster to its significance.—Arthur Eddington,The Nature of the Physical World. (shrink)

Substantially increased wealth inequality across the developed world has prompted many philosophers, economists and legal theorists to support comprehensive taxes on all forms of wealth. Proposals include levying taxes on the basis of total wealth, or alternatively the change in the value of capital holdings measured from year-to-year. This contrasts with most existing policies that tax capital assets at the point they are transferred from one beneficiary to another through sale or gifts. Are these tax reforms likely to meet their (...) aims of greater economic and political equality? We argue that these policies are likely to fail because, following neoclassical economic theory, they are based on a conception of capital as possessing given values in what amounts to a static equilibrium. This mischaracterizes the dynamic and subjective character of market economies and the contested value of real instantiations of capital goods. This makes them very difficult, often impossible, to value apart from at the point of voluntary transfer or profit realization. This means most taxes levied on a mark-to-market basis will be arbitrary and unfair. We propose alternative policies based on an income realization approach to taxation that are more likely to curb excessive wealth holdings. This includes introducing international treaties that prohibit preferential tax treatment for individual companies and specific sectors, and broadening the income tax base to include the imputed rent of personal housing wealth. (shrink)

We define an evolutionary process of “economic Darwinism” for playing the field, symmetric games. The process captures two forces. One is “economic selection”: if current behavior leads to payoff differences, behavior yielding lowest payoff has strictly positive probability of being replaced by an arbitrary behavior. The other is “mutation”: any behavior has at any point in time a strictly positive, very small probability of shifting to an arbitrary behavior. We show that behavior observed frequently is in accordance with “evolutionary (...) class='Hi'>equilibrium”, a static equilibrium concept suggested in the literature. Using this result, we demonstrate that generally under positive (negative) externalities, economic Darwinism implies even more under- (over-)activity than does Nash equilibrium. (shrink)

Substantially increased wealth inequality across the developed world has prompted many philosophers, economists and legal theorists to support comprehensive taxes on all forms of wealth. Proposals include levying taxes on the basis of total wealth, or alternatively the change in the value of capital holdings measured from year-to-year. This contrasts with most existing policies that tax capital assets at the point they are transferred from one beneficiary to another through sale or gifts. Are these tax reforms likely to meet their (...) aims of greater economic and political equality? We argue that these policies are likely to fail because, following neoclassical economic theory, they are based on a conception of capital as possessing given values in what amounts to a static equilibrium. This mischaracterizes the dynamic and subjective character of market economies and the contested value of real instantiations of capital goods. This makes them very difficult, often impossible, to value apart from at the point of voluntary transfer or profit realization. This means most taxes levied on a mark-to-market basis will be arbitrary and unfair. We propose alternative policies based on an income realization approach to taxation that are more likely to curb excessive wealth holdings. This includes introducing international treaties that prohibit preferential tax treatment for individual companies and specific sectors, and broadening the income tax base to include the imputed rent of personal housing wealth. (shrink)

Since economies are dynamic processes driven by creativity, social norms, and emotions as well as rational calculation, why do economists largely study them using static equilibrium models and narrow rationalistic assumptions? Economic activity is as much a function of imagination and social sentiments as of the rational optimisation of given preferences and goods. Richard Bronk argues that economists can best model and explain these creative and social aspects of markets by using new structuring assumptions and metaphors derived from (...) the poetry and philosophy of the Romantics. By bridging the divide between literature and science, and between Romanticism and narrow forms of Rationalism, economists can access grounding assumptions, models, and research methods suitable for comprehending the creativity and social dimensions of economic activity. This is a guide to how economists and other social scientists can broaden their analytical repertoire to encompass the vital role of sentiments, language, and imagination. (shrink)

The "trembling balance" in Lawrence's work, considered either as theoretical system or in its phenomenological form, is characterized by the dynamic qualities of interrelatedness and flux. Cowan shows that, in Lawrence's conception, the dynamic experience of life's quickness necessarily involves giving up static equilibrium in the ebb and flow of human consciousness between self and other, bringing about a sequence of stability, instability, resilience, and creative change. Lawrence's conception of art as a recreation of the "trembling balance" of (...) life is explored in his treatment of the figure of the artist in a number of his major novels. Because his conception of art is biologically based, Lawrence locates the aesthetic balance he seeks to establish between blood consciousness and spiritual consciousness firmly in the body, most often in the imagery of the male body. Lawrence identifies with Melville, who was for him an example of the "true artist" as myth-maker, reconciling Christian and pagan consciousness in an organic symbolism rooted in unconscious experience. Cowan provides a critical study of Lawrence's dualism, dealing with ideas and issues that were intensely personal for Lawrence. (shrink)

To date, economics has failed to develop a useful theory of entrepreneurship because of its inability to break out of the static equilibrium framework and the modeling of success/failure as a 0-1 variable. Entrepreneurship research also has not achieved this task due to its preoccupation with the quest for “the successful entrepreneur” and/or the successful firm. This essay calls for a new vocabulary for entrepreneurship, consisting of (1) a plural notion of the entrepreneurial process as a stream of (...) successes and failures, wherein failure management becomes the key science of entrepreneurship; (2) an effectual notion of bringing together particular entrepreneurs and particular environments through creative action; and (3) a contingent notion of aspirations that places imagination at the center stage of economics. Together, the new vocabulary allows us to ask new questions and develop new approaches that allow entrepreneurship to tackle the central task of imagination in economics, i.e., to create from the society we have to live in, the society we want to live in. (shrink)

In The Crisis of Global Capitalism, George Soros claims that the international financial economy is inherently unstable, and that while economists have failed to recognize this because of their commitment to static equilibrium theory, politicians have failed to stabilize the global economy because of their commitment to an unquestioned faith in the complete efficiency of laissez faire. While Soros is right to argue that market participants’ expectations about the future can cause instability, he is wrong to maintain that (...) this has gone unrecognized by economists, and his notion that we live in a world of economic laissez faire is equally mistaken. Indeed, his own analysis of the Asian financial crisis points to the “moral hazard” created by expectations of government intervention, rather than to laissez faire, as the culprit. (shrink)

1.- Introduction: articulating Hayek’s evolutionary argument with his socialist calculation dispute I completely agree with Bruce Caldwell (Caldwell 1988b: 74-75; Caldwell 1988a) that it is precisely within the conceptual and theoretical framework of the debate on the possibility of socialist calculation that Hayek definitively breaks with the standard static equilibrium approach to the market economy and finds out that the central problem of economics is related to the complex question of social coordination. From the Hayekian standpoint, this problem (...) cannot be solved without articulating a genuine theory about the role and the use of knowledge in society.1 This forms the hard core of what I will call the Hayekian theoretical argument. But one can find a much different kind of argument in Hayek, i.e. an evolutionary argument. I will characterize this argument as the Hayekian empirical argument. Hayek first exposed the essential elements of this genuine argument systematically in Law, Legislation and Liberty (see especially Hayek 1973). But in Hayek’s last book (Hayek 1988), socialism is still analyzed from this evolutionary standpoint , and as such socialism is considered by Hayek to be the major problem not only of economic theory but also, more globally, of Western civilization itself. In that book, published the year before the Soviet Union collapsed, Hayek showed himself to be absolutely confident that economic analysis could prove that socialism was not only a social blunder and a political failure, but above all a formidable scientific error. My reading of Hayek’s work is that this evolutionary argument has to be linked to the first one, which is of a more theoretical nature as far as economics is concerned. Indeed, while the evolutionary argument puts forward a completely different conceptual framework tightening the theoretical argument, it first of all displaces the gist of Hayek’s claim against socialism.. (shrink)

To date, economics has failed to develop a useful theory of entrepreneurship because of its inability to break out of the static equilibrium framework and the modeling of success/failure as a 0-1 variable. Entrepreneurship research also has not achieved this task due to its preoccupation with the quest for “the successful entrepreneur” and/or the successful firm. This essay calls for a new vocabulary for entrepreneurship, consisting of (1) a plural notion of the entrepreneurial process as a stream of (...) successes and failures, wherein failure management becomes the key science of entrepreneurship; (2) an effectual notion of bringing together particular entrepreneurs and particular environments through creative action; and (3) a contingent notion of aspirations that places imagination at the center stage of economics. Together, the new vocabulary allows us to ask new questions and develop new approaches that allow entrepreneurship to tackle the central task of imagination in economics, i.e., to create from the society we have to live in, the society we want to live in. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Eleatic BergsonDonna Jones (bio)Suzanne Guerlac. THINKING IN TIME: AN INTRODUCTION TO HENRI BERGSON. Ithaca: Cornell UP 2006. [TT]In her Thinking in Time: An Introduction to Henri Bergson Suzanne Guerlac reminds her readers that the metaphysician has indeed been the subject of many hatreds, as the Bergsonist Gilles Deleuze once noted. But from this taut philosophical study one cannot easily make out any possible grounds for enmity; nor were (...) any expressed in the special Bergson issue of Modern Literary Notes edited by Guerlac. In this short review essay I shall voice some of that historic criticism, especially in regard to the social and political implications of his thought. Guerlac’s study may also win its own opponents for its sharp criticisms of Deleuze’s interpretations of Bergson and (in her reading) comically machinic view of life [TT 176–87]. This alone makes the book worth reading; it is also exhaustively researched, and I cannot remember learning as much from the footnotes of any other book.Bergson is presented here as a great metaphysician on the nature of time and space, the philosophical father of nonlinear science, and a theorist of concrete and affective individuality. Rejecting implicitly Leszek Kolakowski’s reading of two Bergsons, Guerlac presents him as neither a cosmologist who opposes life and matter nor an existentialist who retrieves consciousness by opposing time to space. Nor does he emerge as a systematic thinker in this study. In the last chapter Guerlac offers a dizzying defense of Bergson for providing the philosophical basis for cultural studies of the qualitative irreducibility of affectual states, the metaphysics of chaos theory, the critique of artificial intelligence, and the rudiments of an aesthetic theory of digital art and virtual reality.All of this follows from the epochal significance of Bergson’s metaphysical distinction between time and space as carefully grounded in the most advanced physics of his time. Guerlac does not discuss in any detail Bergson’s vitalist critiques of Darwinian biology in Creative Evolution, the work through which the metaphysical arsonist fired the modernist imagination in diverse, contradictory, and at times violent ways.1 Nor does she explore the occult and mystical themes that run throughout Bergson’s work and informed his personal and professional associations.In fact, Guerlac writes: “An explicit appeal to the social values of mystical experience in this study [The Two Sources of Morality and Religion] appeared to vindicate those who had criticized Bergson all along for being simply a mystic. And yet the title of the work, and the basis for the notion of closed and open societies, derive from scientific, not mystical discourse. They refer us to an opposition between closed and open systems in Sadi Carnot’s theories of thermodynamics” [TT 9]. Yet Bergson bases the opposition [End Page 21] between closed and open societies not in thermodynamics but in sociobiology. Having sociobiological reasons to believe in the power of the myths of closed morality on the human mind—groups that had instilled loyalty through myth and ritual had been more successful in the course of evolutionary history; that is, humans susceptible to myth have been successful in a positivist Darwinian sense—he called for the cooptation of such susceptibility by those myths and rituals that instilled loyalty to humanity as such. Humanity could dynamically extend the scope of sociability rather than follow the roles and customs that maintained a closed society in static equilibrium. Though Bergson would later courageously risk pneumonia to stand as an old man in the cold rain to register as a Jew in Vichy France, he claimed in this last book from 1932 that the only complete inspiration for universal openness could be found in Christian mysticism and mythology [Two Sources 227]. He explicitly criticized the insularity of the Judaic religion (and caricatured Eastern forms of mysticism). In other words, Bergson put his faith in Christian mystics alone and thus invited the charge of having laid the foundation for mystical and intolerant leadership.Bergson’s universal humanism also crashed on the limits of colonial racism. In considering closed primitive societies, Bergson called attention to missionary stories full of detailed accounts of childish and monstrous deeds. He implored his... (shrink)

Abstract In The Crisis of Global Capitalism, George Soros claims that the international financial economy is inherently unstable, and that while economists have failed to recognize this because of their commitment to static equilibrium theory, politicians have failed to stabilize the global economy because of their commitment to an unquestioned faith in the complete efficiency of laissez faire. While Soros is right to argue that market participants? expectations about the future can cause instability, he is wrong to maintain (...) that this has gone unrecognized by economists, and his notion that we live in a world of economic laissez faire is equally mistaken. Indeed, his own analysis of the Asian financial crisis points to the ?moral hazard? created by expectations of government intervention, rather than to laissez faire, as the culprit. (shrink)

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). -/- In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where (...) the equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolò Fontana, better known as Tartaglia (1500?–1557), wrote the treatise Quesiti et inventioni diverse (1546). -/- This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia’s lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. -/- This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists. (shrink)

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should (...) consider one action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame. (shrink)

The notion of Nash equilibrium in static oligopoly games is based on the assumption that each firm knows its entire demand curve (and, therefore, its entire profit function). It is much more likely, however, that firms only have some idea of the outcome of small price variations within some relatively small interval of prices. This is because firms can only learn their demand functions through price experiments and if they are risk-averse and/or have a low discount factor, they (...) will be unwilling to engage in extensive price experiments involving large variations in price. We can therefore expect firms to experiment through small price variations and stop when they reach a price such that no small deviation.. (shrink)

We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same (...) assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions. (shrink)

This book presents a theoretical treatment of externalities, public goods, and club goods. The new edition updates and expands the discussion of externalities and their implications, coverage of asymmetric information, underlying game-theoretic formulations, and intuitive and graphical presentations. Aimed at well-prepared undergraduates and graduate students making a serious foray into this branch of economics, the analysis should also interest professional economists wishing to survey recent advances in the field. No other single source for the range of materials explored is currently (...) available. Topics investigated include Nash equilibrium, Lindahl equilibria, club theory, preference-revelation mechanism, Pigouvian taxes, the commons, Coase Theorem, and static and repeated games. The authors use mathematical techniques only as much as necessary to pursue the economic argument. They develop key principles of public economics that are useful for subfields such as public choice, labor economics, economic growth, international economics, environmental and natural resource economics, and industrial organization. (shrink)

Political theorists study the attributes of desirable social-moral states of affairs. Schaefer (forthcoming) aims to show that "static political theory" of this kind rests on shaky foundations. His argument revolves around an application of an abstruse mathematical theorem -- Kakutani's fixed point theorem -- to the social-moral domain. We show that Schaefer has misunderstood the implications of this theorem for political theory. Theorists who wish to study the attributes of social-moral states of affairs should carry on, safe in the (...) knowledge that Kakutani's theorem poses no threat to this enterprise. (shrink)

The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this article, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the second (...) law embodies. I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role—rather than the role of the traditional ‘holy grail’ as described by Callender. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

Game theory has a prominent role in evolutionary biology, in particular in the ecological study of various phenomena ranging from conflict behaviour to altruism to signalling and beyond. The two central methodological tools in biological game theory are the concepts of Nash equilibrium and evolutionarily stable strategy. While both were inspired by a dynamic conception of evolution, these concepts are essentially static—they only show that a population is uninvadable, but not that a population is likely to evolve. In (...) this article, we argue that a static methodology can lead to misleading views about dynamic evolutionary processes. We advocate, instead, a more pluralistic methodology, which includes both static and dynamic game theoretic tools. Such an approach provides a more complete picture of the evolution of strategic behaviour. 1 Introduction2 The Equilibrium Methodology3 Common Interest Signalling3.1 Lewis’s signalling game3.2 Static analysis3.3 Dynamic analysis4 The Sir Philip Sidney Game4.1 Static analysis4.2 Other equilibria4.3 Dynamic analysis5 Related Literature6 Static and Dynamic Approaches. (shrink)

One of the central questions of economics relates to the coordination of individual units within a large organization to achieve the central objectives of that organization. This book examines the problems involved in allocating resources in an economic system where decision-making is decentralized into the hands of individuals and individual enterprises. The decisions made by these economic agents must be coordinated because the input decisions of some must eventually equal the output decisions of others. Coordination arises naturally out of the (...) mathematical theory of optimization but there is still the question of how it can be achieved in practice with dispersed knowledge. The essays here explore the many facets of this problem. Nine papers are grouped under the title 'Economies with a single maximand'. They include papers on static and dynamic optimization, decentralization within firms, and nonconvexities in optimizing problems. Fourteen papers are concerned with 'Economies with multiple objectives'. Among the topics covered here are stability of competitive equilibrium, stability in oligopology, and dynamic shortages. The final part of the book includes three papers on informational efficiency and informationally decentralized systems. Leonid Hurwitcz is the Nobel Prize Winner 2007 for The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, along with colleagues Eric Maskin and Roger Myerson, for his work on the effectiveness of markets. (shrink)

This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on (...) the interaction of payoff asymmetries and noisy introspection about others’ decisions. (shrink)

Darwin's theory of evolution brought to an end the static view of nature. It was no longer possible to think of species as immortal, with secure places in nature. Fluctuation of population could no longer be thought of as occurring within definite limits which had been set at the time of creation. Nor was it any longer possible to generalize from the differential reproductive potentials, or from a few cases of mutualism between species, that everything in nature was “fitted (...) to produce general ends, and reciprocal uses.” 134 The appeal to “design” could no longer be substituted for answers to questions concerning animal demography. Instead, the dynamics of a population had to be viewed as the outcome of species' struggle against animate and inanimate factors in the environment. Both the members of a species and the environmental factors tend to vary randomly, and therefore neither evolution nor population dynamics could be fully understood alone. For this reason Darwin's linking of the two subjects was inevitable and not merely an historical accident. Since Darwin had shown that no automatic equilibrium existed, he demonstrated the importance of closer study of the causes of population dynamics and extinction. He also indicated that an understanding of population depends upon the development of a broad knowledge in ecology.Viewed from another direction, Darwin's work ended the early modern era of population studies by clarifying three interrelated problems which were important for understanding population: extinction, distribution, and the nature of species. The components of his answer had been discussed in the eighteenth century, but there had not existed enough evidence for the completion of the revolution in thought which had then begun. At the beginning of the nineteenth century, Playfair found the evidence for extinction conclusive, and, in spite of Lamarck, Curvier convinced the scientific world that there could no longer be any doubt about it. This was a step the importance of which, with his limited knowledge of biogeography and population, Cuvier could not have fully realized. Lamarck attempted, with his evolutionary theory, to circumvent the necessity for admitting extinction, but he overestimated the adaptability of organisms and in doing so he underestimated the importance of competition and the whole field of ecology. On the other hand, he was not willing to let questions such as the origin of species remain taboo to science. The origin of species was a biogeographical as well as a paleontological question. Humboldt correlated environment with the distribution of species and conveyed the impression that plant communities are subject to change. De Candolle, following the lead of Linnaeus and Humboldt, emphasized the ecological aspects of biogeography, not only the importance of habitat and range, clearly showing the ecological effects of competition. The entomologists Kirby and Spence took a faltering step toward understanding the relationship between population and ecological role, but they fell short of any significant new conclusions. Neither they nor Swainson could fully comprehend the new perspective of De Candolle.Lyell was able to bring together the evidence from these three lines of investigation and weave them into an important synthesis that almost accomplished that Darwin later did. Although opposing Lamarck's theory of evolution, Lyell had a dynamic view of ecology. He realized that population dynamics offered an important key to the understanding of biogeography. Since he knew that species become extinct, he investigated closely the factors which could either preserve or extinguish species. While explaining these factors, he described the interrelationships of species in greater detail than had ever been done before. Forbes continued to develop Lyell's ecological concepts, and his first-hand field experience enabled him to describe biotic communities more concretely than Lyell had.Having the advantages of Lyell's understanding and his own experience from a global voyage, Darwin could take the final step from the static to the dynamic concept of life. He had seen populations fluctuating and also fossil species in South America, and on the Galapagos Islands he had encountered a biogeographical problem that could not be credibly solved without the idea of evolution. However, the bare idea of evolution did not fully answer his questions. He sought physiological causes of extinction before he read Malthus and realized that De Candolle and Lyell had correctly emphasized the importance of competition. Darwin found that, in order to understand evolution, he needed to improve his understanding of ecology. He wanted to know when populations were most easily decimated, how extensive were competition and cooperation, what effects parasites have upon populations, and what changes occur in biotic communities when a species is either added or subtracted. He contributed to some extent to answering these questions. Though there remained much for others to do, there was now a new and more secure theoretical framework within which later studies could be interpreted. As Ernst Mayr has observed, Darwin's “consistent thinking in terms of population has had an impact on biological theory and practice which is second only to his sponsorship of natural selection as the mechanism of evolution.” 135. (shrink)

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, individual (...) configurations are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. -/- For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. -/- The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. -/- I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. -/- I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism. (shrink)

We examine the evolution of the concept of stability in community ecology, arguing that biologists have moved from an emphasis on biotic communities characterized by static balance, to one of dynamic balance (returning to equilibrium after perturbation), to the current concept of stability as persistence. Using Wimsatt's (1987) analysis of how false models can often lead to better ones, we argue that failed attempts to link complexity with stability have significant heuristic value for community ecologists. Nevertheless, we argue (...) that, (A) because there is no common characteristic that stability terms presuppose, community ecology might be better served by abandoning the concept of stability and by employing instead specific terms such as 'persistence', 'resistance', and 'variability'. (B) The current emphasis (of stability terms) on persistence of species provides little basis for explaining possible mechanisms that might account for persistence. (shrink)

We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; however when the penalty is (...) high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents. (shrink)

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity (...) can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies “free enterprise” with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it. (shrink)

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where the (...) equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolò Fontana, better known as Tartaglia (1500?-1557), wrote the treatise Quesiti et inventioni diverse (1546). This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia's lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists. (shrink)

In this article three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points—points below which they consider payoffs to be losses—are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000; Int. J. Game Theory 29(2):269) under the name of ‘myopic loss aversion equilibrium.’ There, the players’ reference points (...) depend on the beliefs about their opponents’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference points are only based on the carriers of the strategies, not on the exact probabilities. In the third type, the safety level loss aversion equilibrium, the reference points depend on the values of the own payoff matrices. Finally, a comparative statics analysis is carried out of all three equilibrium concepts in 2 × 2 bimatrix games. It is established when a player benefits from his opponent falsely believing that he is loss averse. (shrink)

It is common practice in intergenerational justice to set fixed thresholds determining what qualifies as justice. Static definitions of how much and what to save for future generations, however, overestimate human epistemological limits and predictive capacity in regard to uncertainty in social- and ecosystems. Long-term predictions cannot account for the inherent range of contingent variables at play, especially according to contemporary theories of punctuated equilibrium. It is argued that policies deliberately testing ecological limits as currently conceived must be (...) excluded from political calculations to minimize current actions from foreclosing future life quality and options. To better reduce harms to present and future generations and support the stability of just institutions (and the stable environments they depend on) as Rawls and others demand, polities can overcompensate resource allocation to environmental sustainability. Focus on reducing environmental harms benefits both current and future generations, reconciling distributive versus intergenerational justice trade-offs. (shrink)

This study aims to evaluate the ideas on the scope and method of economics of Joseph Schumpeter who is one of the important economists of the 20th century. The study consists of four sections: In the first section we underline the interesting points of his life to understand the roots, background, or 'vision' of his thought system. In the second section, we will examine his methodological views that he asserted in his first (but translated into English only in 2010) book. (...) Third section will be concerned with his 'analysis of economics' which refers to his critics of Leon Walras's general equilibrium analysis (as static) and his own alternative (dynamics analysis of capitalist economies) about the central subject matter of economics. In the fourth section we will treat his approach about the development/evolution process of economic thought in time. The study concludes with a brief assessment: Schumpeter is one of the rare economists who can build his own thought system in the history of economics, and he embraced a pluralist perspective in the field of the methodology of economics. (shrink)

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity (...) can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies “free enterprise” with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it. (shrink)

Biology is in a unique position among the natural sciences. It is not simply complex physics and chemistry, for living organisms have a psychological as well as a physical side. Even as physical systems their character is highly special, largely because their material substance is continually changing; perhaps it was from them that Heraclitus derived his idea that all is flow. The comparison with vortexes and candle flames is an old one. Wilhelm Ostwald included living organisms in his class of (...) “stationary systems”: they represent not a static but a kinetic equilibrium, what we now often call a “steady state”; there is a balance of constitutive and dissipative processes. Materials and energy converge to the living center, undergo there characteristic transformations, among which complex chemical and structural syntheses are conspicuous, and are again distributed at random to the surroundings. The living organism is thus the seat of a special type of physical and chemical activity found nowhere else in nature, and it is significant that this is associated with psychical activity—demonstrably in the higher organisms, by implication in the lower. (shrink)

This paper introduces a receiver who perceives ambiguity in a binary model of Bayesian persuasion. The sender has a well-defined prior, while the receiver considers an interval of priors and maximizes a convex combination of worst and best expected payoffs. We characterize the sender’s optimal signal and find that the receiver’s payoff differences across states given each action, play a fundamental role in the characterization and the comparative statics. If the sender’s preferred action is the least sensitive one, then the (...) sender’s equilibrium payoff, as well as the sender’s preferred degree of receiver ambiguity, is increasing in the receiver’s pessimism. We document a tendency for ambiguity-sensitive receivers to be more difficult to persuade. (shrink)

Summary This article intends to propose new hypotheses concerning the origin of the ?Principe général? of mechanics of Jean Le Rond D'Alembert expressed in its Traité de dynamique in 1743. The examination of the statics of Pierre Varignon and its inheritance suggests that D'Alembert retains, through a case of oblique collision on a hard surface, a method of decomposition and equilibrium of forces which is close to its principle. On the other hand, this principle requires a definition of the (...) equilibrium widely spread in the 17th and 18th centuries, D'Alembert seeming then more to innovate from an epistemological point of view that on a technical one. Finally, the determination of rules of collision based at the same time on decompositions of movements at the level of the centre of mass and on appeal to a principle of relativity constitutes a know-how at the beginning of the 18th century which can be moved closer to methods developed by D'Alembert. These three aspects try then to replace the science of D'Alembert in a context by insisting on the essential role of the collisions of body and on that of the notion of equilibrium concerning the birth of its principle. (shrink)

Recent years have seen a certain impatience with John Rawls's approach to political philosophy and calls for the discipline to move beyond it. One source of dissatisfaction is Rawls's idea of a well-ordered society. In a recent article, Alex Schaefer has tried to give further impetus to this movement away from Rawlsian theorizing by pursuing a question about well-ordered societies that he thinks other critics have not thought to ask. He poses that question in the title of his article: “Is (...) Justice a Fixed Point?.” Though Schaefer is critical of Rawlsian political theorizing, I shall contend that his arguments also suggest two paths forward for those who would follow the Rawlsian approach. First, the intellectual devices Schaefer deploys help those who would continue the Rawlsian project to see, and precisely to chart, the next step that that project needs to take—a step necessitated by a concession Rawls himself made late in the development of political liberalism. Second, the clarity and economy with which Schaefer lays out his alternative to the Rawlsian approach make it possible to state some fundamental Rawlsian challenges to a form of theorizing that has considerable appeal to many critics of that approach. (shrink)

The hanging of the mobile aloft was annually performed with a solemnity and care suited to so important a matter. For each year, as it was resurrected from its storage place, it hung foolishly askew, demoralized by vicissitude, like a drunkard's hat crushed out of shape. Not that it had not still an equilibrium, a static balance, which it would assume and, if disturbed, would assume again, as if to declare idiocy alone immortal. It did not wait, in (...) order to have an equilibrium, for an artful hand to give it one. Such equilibrium as it had, from the accidental concert of its parts, it had with the indifferent equanimity of all things merely physical. Beauty was its accident, as idiocy also was its accident. It was as innocent of virtue as it was innocent of sin: it knew no propriety, therefore deserted none. I admired in it only what I demanded of it, a virtue of which it knew nothing. Yet, for my part, I permitted myself no such egotist reflection. I regarded it all as the contrivance of the hand which adjusted it. In my child's world, that was the secret of my mother's hand, which no other sought to compete with, much less to penetrate. She knew, at least her hand knew, that of all of the possible equilibria which were available equally for choice, there was one special equilibrium needed, only one which was alive, resonant, essential to the production of that effect to which it intricately ministered. That equilibrium was indispensable to the music which the mobile gave forth, its beginning and its end, the poise from which its movement issued, the cadence in which it came with perfect finality to rest. (shrink)