1. Reasoning about action and change, or more generally reasoning about dynamic systems, is not only central to knowledge representation and reasoning but at the heart of computer science (Fisher e...

ABSTRACT Against empiricist and rationalist prejudices concerning the nature of issues related to “mental health,” this article offers a phenomenological account of identity as developed in a meaningful system with the environment or world. Drawing on the work of Merleau-Ponty and Dewey, I argue that behavioral and emotional health and illness must be understood in terms of the plasticity or rigidity, respectively, of the individual's responses in the face of new and threatening environmental demands. However, individual plasticity and rigidity are (...) not given qualities of the individual but are themselves developed in healthy or unhealthy interpersonal environments. I discuss three cases of emotional and behavioral trouble in order to explore the manner in which unhealthy self-environment systems can undermine individuals' powers of adaptability and growth. (shrink)

In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are (...) found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system. (shrink)

Economic explanations of inequality in liberal economies often appeal to social norms. This article argues that recent economic policies and institutional interventions, in favor of deregulation and away from participatory practices in both the political and economic spheres, have elicited norms that increasingly resemble those of the economic theory that has informed these interventions. This has altered the social ethos in an inegalitarian direction—individuals are more likely to conceive of themselves as acquisitive maximizers in their daily life, and there has (...) been a reduction in the number of institutional settings for people to deliberate on their values, commitments, and other priorities. (shrink)

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)

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)

Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and (...) harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production. (shrink)

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the unstable (...) particles. (shrink)

Elgin has presented an extensive defence of reflective equilibrium embedded in an epistemology which focuses on objectual understanding rather than ordinary propositional knowledge. This paper has two goals: to suggest an account of reflective equilibrium which is sympathetic to Elgin’s but includes a range of further developments, and to analyse its role in an account of understanding. We first address the structure of reflective equilibrium as a target state and argue that reflective equilibrium requires more than (...) an equilibrium in the sense of a coherent position. On the one hand, the position also needs to be stable between a ‘conservative’ pull of input commitments and a ‘progressive’ pull of epistemic goals; on the other hand, reflective equilibrium requires that enough of the resulting commitments have some credibility independent of the coherence of the position. We then turn to the dynamics of reflective equilibrium, the process of mutual adjustment of commitments and theories. Here, the most pressing internal challenges for defenders of reflective equilibrium arise: to characterize this process more exactly and to explain its status in relation to reflective equilibrium as a target state. Finally, we investigate the role of reflective equilibrium in Elgin’s account of understanding and argue that objectual understanding cannot be explained in terms of reflective equilibrium alone. An epistemic agent who understands a subject matter by means of a theory also needs to be able to use this theory and the theory needs to meet some external rightness condition. (shrink)

This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in (...) which such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. (...) The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system. (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 argue that the Soros account of reflexivity does not provide a clear-cut distinction between a social science such as economics and the physical sciences. It is pointed out that the participants who attempt to learn from refutations of conjectures in the Soros world are likely to be haunted by the Duhem–Quine problem of conjointness of hypotheses and unfocused refutation. On a more constructive note, we argue that models of inductive learning, in which participants form conjectures on the basis of (...) strictly limited information sets, can capture the basic thrust of the Soros position. The conjectures are in motion, as the participants attempt to avoid those that are systematically wrong, and there is something vague and uncertain about what can be learned from experience and refutations. The only notion of market efficiency in this world is one contingent on the strictly limited and varied information sets in play. Finally we present a mathematical model and numerical simulations that help justify the causal relationship between reflexivity and far-from-equilibrium dynamics postulated by Soros. (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)

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)

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-epsilon-equilibrium. This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.

This paper is reporting on electronic implementation of a three-dimensional autonomous system with infinite equilibrium point belonging to a parabola. Performance analysis of an adaptive synchronization via relay coupling and a hybrid steganography chaos encryption application are provided. Besides striking parabolic equilibrium, the proposed three-dimensional autonomous system also exhibits hidden chaotic oscillations as well as hidden chaotic bursting oscillations. Electronic implementation of the hidden chaotic behaviors is done to confirm their physical existence. A good qualitative agreement is shown (...) between numerical simulations and OrCAD-PSpice results. Moreover, adaptive synchronization via relay coupling of three three-dimensional autonomous systems with a parabolic equilibrium is analysed by using time histories. Numerical results demonstrate that global synchronization is achieved between the three units. Finally, chaotic behavior found is exploited to provide a suitable text encryption scheme by hidden secret message inside an image using steganography and chaos encryption. (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)

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Several authors have recently argued that the excessive focus on equilibrium models in mainstream economic analysis prevents economists from providing accurate representations of the complex and dynamic nature of real economic systems. In response, this paper argues the following. Many economic systems are the products of deliberate and centralized human design. People can and do build and support structures, such as social institutions, aiming to enhance the predictability of economic systems, and thus to move them toward being (...) class='Hi'>equilibrium systems. This provides a reason to think that many economic systems can be represented by equilibrium models. (shrink)

This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie–Bohm–Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie–Bohm–Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc (...) assumption that the initial distribution of particle locations has to be identical to the initial probability distribution prescribed by the system’s initial wave function. The results presented in this paper moreover suggest that the intrinsically stochastic nature of Bell’s formulation, which is arguable most naturally formulated on an underlying discrete space-time, is sufficient to ensure dynamical relaxation to quantum equilibrium for a large class of quantum systems without the need to introduce coarse-graining or any other modification in the formulation. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to (...) the largest macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

This article analyzes the temporal single-system interpretation (TSSI) of Marx’s economics. From a methodological viewpoint, the TSSI lacks both a clear definition of equilibrium and a rigorous analysis of disequilibrium dynamics, and the dynamic framework is incomplete. From a substantive viewpoint, temporal single-system (TSS) claims are trivially obtained by assuming that goods exchange at values, apart possibly from out-of-steady-state random deviations. Finally, the proof of the law of the tendential fall in the profit rate is tautologically true, but (...) its theoretical relevance is unclear. (shrink)

Protein turnover (PT) has been formally defined only in equilibrium conditions, which is ill‐suited to quantify PT during dynamic processes that occur during embryogenesis or (extra) cellular signaling. In this Hypothesis, we propose a definition of PT in an out‐of‐equilibrium regime that allows the quantification of PT in virtually any biological context. We propose a simple mathematical and conceptual framework applicable to a broad range of available data, such as RNA sequencing coupled with pulsed‐SILAC datasets. We apply (...) our framework to a published dataset and show that stimulation of mouse dendritic cells with LPS leads to a proteome‐wide change in PT. This is the first quantification of PT out‐of‐equilibrium, paving the way for the analysis of biological systems in other contexts. (shrink)

In this paper, I draw a parallel between the stability of physical systems and that of economic ones, such as the US financial system. I argue that the use of equilibrium assumptions is central to the analysis of dynamic behavior for both kinds of systems, and that we ought to interpret such idealizing strategies as footholds for causal exploration and explanation. Our considerations suggest multi-scale modeling as a natural home for such reasoning strategies, which can provide a backdrop (...) for the assessment and prevention of financial crises. Equilibrium assumptions are critical elements of the epistemic scaffolding that make up multi-scale models, which we should understand as a means of constructing explanations of dynamic behavior. (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)

The aim of the paper is the construction of a distributional model which enables the study of the evolutionary dynamics that arise for symmetric games, and the equilibrium selection mechanisms that originate from such processes. The evolution of probability distributions over the state variables is studied using the Fokker-Planck diffusion equation. Equilibrium selection using the ’’basin of attraction’’ approach, and a selection process suggested by Pontryagin are contrasted. Examples are provided for all generic 2-person symmetric binary choice games. (...) JEL Classification: C78.. (shrink)

Brian Skyrms constructs a theory of "dynamic deliberation" and uses it to investigate rational decision-making in cases of strategic interaction. This illuminating book will be of great interest to all those in many disciplines who use decision theory and game theory to study human behavior and thought. Skyrms begins by discussing the Bayesian theory of individual rational decision and the classical theory of games, which at first glance seem antithetical in the criteria used for determining action. In his effort (...) to show how methods for dealing with information feedback can be productively combined, the author skillfully leads us through the mazes of equilibrium selection, the Nash equilibria for normal and extensive forms, structural stability, causal decision theory, dynamic probability, the revision of beliefs, and, finally, good habits for decision. The author provides many clarifying illustrations and a handy appendix called "Deliberational Dynamics on Your Personal Computer." His powerful model has important implications for understanding the rational origins of convention and the social contract, the logic of nuclear deterrence, the theory of good habits, and the varied strategies of political and economic behavior. (shrink)

To establish the evaluation index system of urbanization innovation level and ecological efficiency, the entropy method is applied to measure the comprehensive index of urbanization innovation level and ecological efficiency, the VAR model is established, and empirical measurement is used to study the internal relationship and dynamic development between urbanization innovation level and ecological efficiency. The empirical results show the following: The overall development of the innovation level in 30 cities in China is uneven, there is a large gap (...) between the urban innovation level in backwards areas and economically developed areas, and there is a certain coupling effect between the urban innovation level and ecological efficiency. There is a long-term dynamic equilibrium relationship between the urban innovation level and ecological efficiency, which will exert certain pressure on the ecological environment in the process of urbanization. However, the continuous improvement of urbanization will have a positive impact on the improvement of the ecological environment. The improvement of ecological efficiency will also promote the improvement of the urban innovation level. Therefore, this paper puts forwards policy suggestions to promote the harmonious development of urbanization and the ecological environment and provides a reference for realizing the balanced development of urbanization and ecological efficiency in China. (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)

The introduction of new technologies in society is sometimes met with public resistance. Supported by public policy calls for “upstream engagement” and “responsible innovation,” recent years have seen a notable rise in attempts to attune research and innovation processes to societal needs, so that stakeholders’ concerns are taken into account in the design phase of technology. Both within the social sciences and in the ethics of technology, we see many interdisciplinary collaborations being initiated that aim to address tensions between various (...) normative expectations about science and engineering and the actual outcomes. However, despite pleas to integrate social science research into the ethics of technology, effective normative models for assessing technologies are still scarce. Rawls’s wide reflective equilibrium is often mentioned as a promising approach to integrate insights from the social sciences in the normative analysis of concrete cases, but an in-depth discussion of how this would work in practice is still lacking. In this article, we explore to what extent the WRE method can be used in the context of technology development. Using cases in engineering and technology development, we discuss three issues that are currently neglected in the applied ethics literature on WRE. The first issue concerns the operationalization of abstract background theories to moral principles. The second issue concerns the inclusiveness of the method and the demand for openness. The third issue is how to establish whether or not an equilibrium has been reached. These issues should be taken into account when applying the methods to real-world cases involving technological risks. Applying the WRE method in the context of engaged interdisciplinary collaboration requires sensitivity for issues of power and representativeness to properly deal with the dynamics between the technical and normative researchers involved as well as society at large. (shrink)

Our scientific theories, like our cognitive structures in general, consist of propositions linked by evidential, explanatory, probabilistic, and logical connections. Those theoretical webs ‘impinge on the world at their edges,’ subject to a continuing barrage of incoming evidence. Our credences in the various elements of those structures change in response to that continuing barrage of evidence, as do the perceived connections between them. Here we model scientific theories as Bayesian nets, with credences at nodes and conditional links between them modelled (...) as conditional probabilities. We update those networks, in terms of both credences at nodes and conditional probabilities at links, through a temporal barrage of random incoming evidence. Robust patterns of punctuated equilibrium, suggestive of ‘normal science’ alternating with ‘paradigm shifts,’ emerge prominently in that change dynamics. The suggestion is that at least some of the phenomena at the core of the Kuhnian tradition are predictable in the typical dynamics of scientific theory change captured as Bayesian nets under even a random evidence barrage. (shrink)

Mixed-strategy equilibria are typically rather unstable in evolutionary game theory. “Monocyclic” games, such as Rock–Paper–Scissors, have only mixed equilibria, some of which are “stable” in the sense that sequential best replies lead to them; yet, even these games are prone to stable cycles under discrete-time simultaneous best replies, giving an unusual equilibrium-selection problem. This article analyzes such games in a random-utility setting where changing strategies is costly, and the speed of the dynamic is, thus, endogenous. The stochastically stable (...) outcome is determined by the cost of switching strategies; when switching costs are high, mixed equilibria are selected, whereas when switching costs are low, cycles are selected. (shrink)

InStabilizing Dynamics Roy Weintraub provides a history of stability theory from the work of Hicks and Samuelson in the late 1930s to the Gale and Scarf counterexamples in the 1960s. Unlike his earlier work in the history of general equilibrium theory this recent contribution is not an attempt to fit the Walrasian program into the narrow framework of some particular philosophy of natural science. Rather, the theme inStabilizing Dynamicsis broadly social constructivist. Simply put, the constructivist view of science is (...) “that scientific knowledge itself is constructed socially, in communities of scientists: Knowledge is constructed, not found”. (shrink)

We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics ; however, the latter states are more likely in cases where honest signalling (...) should apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium. (shrink)

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning (...) which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation. (shrink)

In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account for (...) the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution. (shrink)

In his prophetic book Amythia, Loyal Rue calls for the construction of bold new myths. Responding to his call in light of scientific arguments for global population equilibrium, this article proposes a model that may function as a surrogate form of myth, one that can motivate our age and future ages. Fortunately, the model is not only powerful but achievable, because policy makers have finally begun to realize how thoroughly the human population impacts on other world dynamics. The problem (...) is reviewed, the relevance of scientific and theological studies bearing on it is shown, and the new model is described. Above all, an effort is made to show how global equilibrium can support Rue's twin requirements for the myth he commissions: namely, a foundation in plausible descriptions of reality, and a compelling normative status. (shrink)

In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it (...) is found that for ω = ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. (shrink)

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is (...) assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities. (shrink)