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We construct a model of innovation diffusion that incorporates a spatial
component into a classical imitation-innovation dynamics first introduced by F.
Bass. Relevant for situations where the imitation process explicitly depends on
the spatial proximity between agents, the resulting nonlinear field dynamics is
exactly solvable. As expected for nonlinear collective dynamics, the imitation
mechanism generates spatio-temporal patterns, possessing here the remarkable
feature that they can be explicitly and analytically discussed. The simplicity
of the model, its intimate connection with the original Bass' modeling
framework and the exact transient solutions offer a rather unique theoretical
stylized framework to describe how innovation jointly develops in space and
time.
Since the Cohen and Levinthal article on absorptive capacity was published, 'the ability to recognize the value of new information, to assimilate it, and apply it to commercial ends' (p. 128) is seen as an essential competence for a firm's long-term performance. However, the way absorptive capacity is actually implemented in firms remains relatively poorly known. The few existing works present absorptive capacity as an essentially linear process, and the way the different phases of this process are actually carried out remains understudied. In order to enhance our understanding of the way firms absorb external knowledge, we gathered data from 23 interviews of managers from three different industrial firms. Our results suggest that, far from being linear, the process displays several feedback loops, both within and between each phase of absorption. In this study, we enrich previous absorptive capacity models.
The process for absorbing knowledge becomes an essential element for innovation in firms and in adapting to changes in the competitive environment. In this paper, we present an improved knowledge diffusion hypernetwork (IKDH) model based on the idea that knowledge will spread from the target node to all its neighbors in terms of the hyperedge and knowledge stock. We apply the average knowledge stock , the variable , and the variance coefficient to evaluate the performance of knowledge diffusion. By analyzing different knowledge diffusion ways, selection ways of the highly knowledgeable nodes, hypernetwork sizes and hypernetwork structures for the performance of knowledge diffusion, results show that the diffusion speed of IKDH model is 3.64 times faster than that of traditional knowledge diffusion (TKDH) model. Besides, it is three times faster to diffuse knowledge by randomly selecting “expert” nodes than that by selecting large-hyperdegree nodes as “expert” nodes. Furthermore, either the closer network structure or smaller network size results in the faster knowledge diffusion.
The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the agents interaction range and (b) a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.
We develop a tractable dynamic model of productivity growth and technology spillovers that is consistent with the emergence of real world empirical productivity distributions. Firms can improve productivity by engaging in in-house R&D, or alternatively, by trying to imitate other firms technologies subject to limits to their absorptive capacities. The outcome of both strategies is stochastic. The choice between in-house R&D and imitation is endogenous, and based on firms profit maximization motive. Firms closer to the technological frontier have less imitation opportunities, and tend to choose more often in-house R&D, consistent with the empirical evidence. The equilibrium choice leads to balanced growth featuring persistent productivity differences even when starting from ex-ante identical firms. The long run productivity distribution can be described as a traveling wave with tails following Zipfs law as it can be observed in the empirical data. Idiosyncratic shocks to firms productivities of R&D reduce inequality, but also lead to lower aggregate productivity and industry performance.
This chapter surveys research on agent-based models used in finance. It will concentrate on models where the use of computational tools is critical for the process of crafting models which give insights into the importance and dynamics of investor heterogeneity in many financial settings.
Study of more than 200 species suggests that the anatomical differences among birds are as big as those among other vertebrates of comparable taxonomic rank. The result is notable because, for more than 100 years, many biologists have believed that birds are more uniform anatomically than other classes of vertebrates. Furthermore, assessment of biochemical and geological evidence suggests that the time scale for bird evolution could be quite short. Hence, birds may share with placental mammals the distinction of having had a high rate of anatomical evolution, compared to that in lower vertebrates. The rate appears to have been very high in songbirds and higher primates and extremely high in the genus Homo. In an attempt to explain such contrasts in rates of anatomical evolution, we advance the hypothesis that in higher vertebrates, behavior, rather than environmental change, is the major driving force for evolution at the organismal level. This hypothesis predicts accelerated anatomical evolution in species composed of numerous mobile individuals with the dual capacity for behavioral innovation and social propagation of new habits. Consistent with this hypothesis, we demonstrate a correlation between relative brain size and rate of anatomical evolution in land vertebrates.
This paper provides a survey on studies that analyze the macroeconomic effects of intellectual property rights (IPR). The first part of this paper introduces different patent policy instruments and reviews their effects on R&D and economic growth. This part also discusses the distortionary effects and distributional consequences of IPR protection as well as empirical evidence on the effects of patent rights. Then, the second part considers the international aspects of IPR protection. In summary, this paper draws the following conclusions from the literature. Firstly, different patent policy instruments have different effects on R&D and growth. Secondly, there is empirical evidence supporting a positive relationship between IPR protection and innovation, but the evidence is stronger for developed countries than for developing countries. Thirdly, the optimal level of IPR protection should tradeoff the social benefits of enhanced innovation against the social costs of multiple distortions and income inequality. Finally, in an open economy, achieving the globally optimal level of protection requires an international coordination (rather than the harmonization) of IPR protection.
We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only
There is much debate about the state of the world. Matt Ridley argues in The Rational Optimist that we can solve problems such as economic crashes,population explosions, climate change and terrorism, of poverty, AIDS, depression and obesity. His trust of capitalism and progress is examined and challenged in this book review.
Since the previous ICMP in 2009 in Prague, there has been considerable progress on the Kardar-Parisi-Zhang equation. Our goal here is to give a very brief discussion of some of the results. More comprehensive surveys are available [1-4]. © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." - Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference.
This paper analyzes how imitation can be a catalyst for innovation-a benefit that is often overlooked in the literature. My research shows that a process of learning to innovate occurs as technology diffuses from a more advanced country to a less developed country; therefore, increasing the recipient country's ability to innovate. I find that the efficiency of labor in the R&D sector of the economy determines whether a country learns how to innovate or not. My research predicts that developing countries that have a healthier and more educated workforce can benefit the most from technology diffusion and are more likely to transition from imitating to innovating. On the other hand, countries that have less efficient R&D workers will continue to imitate products from more developed countries instead of inventing new products. Both the level and growth rate of output and TFP increase if a country manages to transition from imitation to innovation. Examining the dynamics that exist between imitation, innovation, and economic growth is important because it can lead to more effective industrial policy. As the results from this paper show, imitation is beneficial and should be supported and encouraged until it becomes feasible and makes sense economically for a country to switch to innovation. Countries that are dependent on technology diffusion should focus on improving the efficiency of their R&D workers if they want to learn how to invent new products. All of the theoretical results of the model are substantiated by empirical evidence.
In a recent model of growth developed by Lucas (Lucas, R., 2009. Ideas and growth. Economica 76, 1–19), a continuum of people interact in a random manner and copy each other’s productive ideas when it is economically beneficial to do so. This paper extends the Lucas model by assuming that each person’s productivity also experiences random shocks due to individual discovery. A nonlinear partial differential equation is derived for the distribution of income, which admits a traveling wave solution representing a growing economy. The growth rate is an increasing function of the rate of imitation. The growth rate is also an increasing but concave function of population size and reaches a plateau in the continuum limit. Hence the scale effect is bounded. The model is extended to account for a nonzero cost of imitation, with similar results. The mathematical tools presented in this paper should prove useful in developing idea-based models of growth.
Stochastic portfolio theory is a flexible framework for analyzing portfolio behavior and equity market structure. This theory was introduced by R. Fernholz in the papers [J. Math. Econ. 31, No. 3, 393–417 (1999; Zbl 0944.91025); Finance Stoch. 5, No. 4, 469–486 (2001; Zbl 1049.91068)] and in the monograph [Stochastic portfolio theory, Applications of Mathematics 48, New York, NY: Springer (2002; Zbl 1049.91067)]. It was further developed by R. Fernholz, I. Karatzas and C. Kardaras [Finance Stoch. 9, No. 1, 1–27 (2005; Zbl 1064.60132)], R. Fernholz and I. Karatzas [“Relative arbitrage in volatility-stabilized markets”, Ann. Finance 1, 149–177 (2005)], A. D. Banner, R. Fernholz and I. Karatzas [Ann. Appl. Probab. 15, No. 4, 2296–2330 (2005; Zbl 1099.91056)] and I. Karatzas and R. Kardaras [Finance Stoch. 11, No. 4, 447–493 (2007; Zbl 1144.91019)]. This theory is descriptive, as opposed to normative; it is consistent with observable characteristics of actual portfolios and markets, and it provides a theoretical tool which is useful for practical applications. As a theoretical tool, this framework offers fresh insights into questions of stock market structure and arbitrage, and can be used to construct portfolios with controlled behavior. As a practical tool, stochastic portfolio theory has been applied to the analysis and optimization of portfolio performance and has been the basis of successful investment strategies for over a decade.
In this paper we provide a generalization of the standard models of the diffusion of a new product. Consumers are heterogeneous and risk averse, and the firm is uncertain about the demand curve: both learn from past observations. The attitude towards risk has important effects with regard to the diffusion pattern. In our model, downward-biased signals to consumers can prevent the success of the product, even if its objective quality is high: a lock-in result. We show in addition that the standard logistic pattern can be derived from the model. Finally, we discuss the asymptotic behavior of the learning dynamics, with regard to the multiplicity and the stability of equilibria, and to their welfare properties.
This paper develops mathematically tractable evolutionary models that can be used to analyze the development of industrial structure as a dynamic process moved by complex interactions among innovations, imitations and investments of satisficing firms striving for survival and growth. It demonstrates that what the industry will approach in the long-run is not a neoclassical equilibrium of uniform technology but at best a statistical equilibrium of technological disequilibria which maintains a relative dispersion of efficiencies in a statistically balanced form. This paper also shows that these evolutionary models can simulate all the macroscopic characteristics of neoclassical growth models without assuming the full rationality of business behavior.
Is more intense product market competition and imitation good or bad for growth? This question is addressed in the context
of an endogenous growth model with “step-by-step” innovations, in which technological laggards must first catch up with the
leading-edge technology before battling for technological leadership in the future. In contrast to earlier Schumpeterian models
in which innovations are always made by outsider firms who earn no rents if they fail to innovate and become monopolies if
they do innovate, here we find: first, that the usual Schumpeterian effect of more intense product market competition (PMC)
is almost always outweighed by the increased incentive for firms to innovate in order to escape competition, so that PMC has
a positive effect on growth; second, that a little imitation is almost always growth-enhancing, as it promotes more frequent neck-and-neck
competition, but too much imitation is unambiguously growth-reducing. The model thus points to complementary roles for competition
(anti-trust) policy and patent policy.
A long-run equilibrium theory of turnover is presented and is shown to explain the important regularities that have been observed by empirical investigators. A worker's productivity in a particular job is not known ex ante and becomes known more precisely as the worker's job tenure increases. Turnover is generated by the exis- tence of a nondegenerate distribution of the worker's productivity across different jobs. The nondegeneracy is caused by the assumed variation in the quality of the worker-employer match.
The author analyzes a sequential decision model in which each decisionmaker looks at the decisions made by previous decisionmakers in taking her own decision. This is rational for her because these other decisionmakers may have some information that is important for her. The author then shows that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. The author then shows that the resulting equilibrium is inefficient. Copyright 1992, the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
The theoretical literature on innovation has been concerned with a single innovation produced by a number of identical agents.
By contrast, we consider a market in which one firm is the current incumbent, while the remaining firms are challengers. Moreover,
we consider a sequence of innovations, so that success does not imply that the successful firm reaps monopoly profits forever
after, but only until the next, better innovation is developed. We begin with a fully optimizing behavioral model and derive
the equivalent of the Schumpeterian “process of creative destruction.” That is, a firm enjoys temporary monopoly power but
is soon overthrown by a more inventive challenger.
The essential point to grasp is that in dealing with capitalism we are dealing with an evolutionary process…The fundamental
impulse that sets and keeps the capitalist engine in motion comes from the new consumers' goods, the new methods of production
or transportation, the new markets, the new forms of industrial organization that capitalist enterprise creates [Schumpeter,
1942, pp. 82–83].
Individuals in a finite population repeatedly choose among actions yielding uncertain payoffs. Between choices, each individual observes the action and realized outcome ofoneother individual. We restrict our search to learning rules with limited memory that increase expected payoffs regardless of the distribution underlying their realizations. It is shown that the rule that outperforms all others is that which imitates the action of an observed individual (whose realized outcome is better than self) with a probability proportional to the difference in these realizations. When each individual uses this best rule, the aggregate population behavior is approximated by the replicator dynamic.Journal of Economic LiteratureClassification Numbers: C72, C79, D83.
This paper develops a simple evolutionary model of innovation and imitation. It analyzes how dynamic interactions between equilibrating force of imitation and disequilibrating force of innovation mold the evolutionary pattern of an industry's state of technology and shows that in this Schumpeterian world the industry will never approach a neoclassical equilibrium with perfect knowlwdge even in the long run. The paper also examines the steady-state efficiency distribution of firms that characterizes the industry's long run and obtains some comparative dynamics results.
The Living Company: Habits for Survival in a Turbulent Business Environment
- A De Geus De Geus
[de Geus, 2002] de Geus, A. (2002). The Living Company: Habits for Survival in a Turbulent Business Environment. Harvard Business School Press.
Linked Research
Working Paper
November 2015