Evolutionary economics goes mainstream: A review of the theory of learning in games

The Theory of Learning in Games by Fudenberg and Levine surveys a key branch of evolutionary economics from a mainstream perspective. Its publication provides an opportunity to reassess the prospects and goals for evolutionary economics.     

Anticipating Nelson and Winter: Jack Downie's theory of evolutionary economic change

An Evolutionary Theory of Economic Change , by Richard Nelson and Sidney Winter continues to have great influence on evolutionary economic thought. While their modeling techniques and the breadth of their vision for evolutionary theorising must be seen as seminal and effective innovation in economic theory, they were not the first inventors of such a theory. Close examination reveals that much of the economic theory was anticipated by Jack Downie whose book, The Competitive Process, was published in 1958. The extent of anticipation is remarkable, with not merely the two elements of population ecology, selection and mutation, but the way in which they are theorised to work being replicated by Nelson and Winter.     

Optimal freeware quality in the presence of network externalities: an evolutionary game theoretical approach

New software products often face difficulty in achieving market penetration. A potential remedy is to offer a freeware version of the software to encourage initial adoption and establish a larger user base for the software, thereby increasing the commercial version's value to adopters in future periods. However, to avoid complete cannibalization of the commercial version, the freeware version's quality must be sufficiently low and the price of the commercial version must not be too high. We model the effect of these two decision variables, price and freeware quality, on the adoption of software using static and evolutionary game theory.     

Correlated equilibrium in evolutionary models with subpopulations

We study a version of the multipopulation replicator dynamics, where each population is comprised of multiple subpopulations. We establish that correlated equilibrium is a natural solution concept in this setting. Specifically, we show that every correlated equilibrium is equivalent to a stationary state in the replicator dynamics of some subpopulation model. We also show that every interior stationary state, Lyapunov stable state, or limit of an interior solution is equivalent to a correlated equilibrium. We provide an example with a Lyapunov stable limit state whose equivalent correlated equilibrium lies outside the convex hull of the set of Nash equilibria. Finally, we prove that if the matching distribution is a product measure, a state satisfying any of the three conditions listed above is equivalent to a Nash equilibrium.     

Stability and trembles in extensive-form games

A leading solution concept in the evolutionary study of extensive-form games is Selten (1983) notion of limit ESS. This note demonstrates that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, I present a novel definition that solves this issue and has appealing properties.     

Asymmetric evolutionary games with non-linear pure strategy payoffs

In this paper, I extend the analytical framework of evolutionary game theory to games with two distinct types of players where the type-specific payoff functions are nonlinear on the right—bi-player-type nonlinear (BNL) evolutionary games. That is, asymmetric games where the payoffs for pairwise interactions are influenced by the ambient frequencies of the pertinent strategies of both types of players.While this paper is motivated by my interest in inter- and intra-gender conflicts of interest in sexual reproduction, BNL games also arise just as naturally in most two-species interactions. Thus, the methodology may provide a novel approach to investigating such classical ecological phenomena as prey–predator/host–parasite interactions and interspecies competition for resources.Finally, given the growing tendency to utilize evolutionary games in economic modeling, a case can be made for the current paper being of interest to traditional game-theoretic modelers in connection with situations such as buyer/seller or employer/employee interaction.     

Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games

The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between quasi-submodularity and global evolutionary stability of strategies for these games, which – apart from being of independent interest – accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy of a quasi-submodular aggregative game must also be globally stable. That is, if one mutant cannot successfully invade a population, any number of mutants can do so even lessThe author is grateful to Ana Ania and Carlos Alōs-Ferrer for comments on an earlier version     

Economic natural selection in Bertrand and Cournot settings

We study economic natural selection in classical oligopoly settings. When underlying pure strategies consist of a finite number of prices, convex monotonic dynamics always converge under a weak condition to the smallest price in the support of the initial state that exceeds marginal cost. When underlying pure strategies consist of a finite number of quantities, monotonic dynamics always converge under a specific condition to a quantity equal or similar to classical Cournot equilibrium.     

A spectrum of equilibration processes in game theory

In game theory, four dynamic processes converging towards an equilibrium are distinguished and ordered by way of agents' decreasing cognitive capacities. In the eductive process, each player has enough information to simulate perfectly the others' behavior and gets immediately to the equilibrium. In epistemic learning, each player updates his beliefs about others' future strategies, with regard to their sequentially observed actions. In behavioral learning, each player modifies his own strategies according to the observed payoffs obtained from his past actions. In the evolutionary process, each agent has a fixed strategy and reproduces in proportion to the utilities obtained through stochastic interactions. All along the spectrum, longer term dynamics makes up for weaker rationality, and physical relations substitute for mental interactions. Convergence, if any, is towards an always stronger equilibrium notion and selection of an equilibrium state becomes more sensitive to context and history. The processes can be mixed if associated to different periods, agents or mechanisms and deepened if obtained by formal reasoning principles.     

A note on control costs and logit rules for strategic games

We consider best response dynamics with endogenous noise based on a finite game in strategic form. A player can reduce the noise level by expending an extra effort and incurring some disutility or control costs. We specify control costs that result in logit adjustment rules. The stochastically stable states of the dynamic process are partial Nash configurations, that is, states where at least one player plays a best response against the others. If the game has a potential, then the stochastically stable states coincide with the Nash equilibria on which the potential is maximized. RID="*" ID="*" Instructive comments of a referee are gratefully acknowledged. Correspondence to:H. Haller     

Schumpeter's theory of economic evolution: a Darwinian interpretation

A general Darwinian framework is employed to arrive at an interpretation of Schumpeter's work that brings out clearly its specific evolutionary aspects. Schumpeter's theory of economic evolution is seen to be still highly relevant to evolutionary economics, because it sheds light on some fundamental issues: the relationship between evolutionary theory and equilibrium analysis, the usefulness of Darwinian theory for economics, and the precise nature of the evolutionary forces at work in economic systems.     

A market game approach to differential information economies

In this paper we recast a differential information economy as a strategic game in which players propose net trades and prices. Pure strategy Nash equilibria are strong and determine both consumption plans and commodity prices that coincide with the Walrasian Expectations equilibria of the underlying economy. The authors acknowledge support by research grants BEC2003-09067-C04-01 (Ministerio de Educación y Ciencia and FEDER), PGIDT04XIC30001PN (Xunta de Galicia) and SA070A05 (Junta de Castilla y León). JP Torres-Martínez is also grateful to CNPq-Brazil and University of Vigo for financial support. We are indebted to N.C. Yannelis for helpful comments and insights.     

Schumpeterian endogenous growth theory and evolutionary economics

In this paper, we aim to discuss whether Schumpeterian models of endogenous growth can accommodate Schumpeters vision of development through creative destruction. Taking a methodological approach, our focus is on individual decision-making, technology, general equilibrium and welfare, and steady state dynamics as the fundamental principles underlying endogenous growth theory. In particular, the Aghion-Howitt model of Schumpeterian growth in various extended versions is analyzed in the light of Schumpeters work. Therefore, we also try to root Schumpeters work in historical context. We find endogenous growth theory far from carrying Schumpeters idea of an evolutionary approach to change and development. Rather the emergence of numerous models of an evolutionary type can be observed to provide for the formal structure appropriate to keeping Schumpeters legacy alive.JEL Classification: B1, B2, B4, O3, O4Corespondence to: Thomas Kuhn     

Satiation in an evolutionary model of structural economic dynamics

This paper presents the problem of satiation of consumption and technology in relation to a model of evolutionary endogenous growth. The model represents an attempt to provide an evolutionary economic micro foundation to Pasinetti's scheme of the structural economic dynamics of an economy that is based on only labour and knowledge. The micro foundation is based on a set of rules that makes endogenous the demand coefficients, the labour coefficients, and the number of available sectors. Through process innovations firms increase their productivities with respect to individual goods, but a growth slowdown takes place unless the benefits from specialisation are exploited at still higher levels. Another cause for slowdown is related to an Engelian hierarchy of goods. As the standard of living grows, existing sectors and consumption goods satiate, so new sectors need to be provided by product innovations in a sufficient pace to keep up with the labour that is displaced from old sectors.     

Learning and behavioral stability An economic interpretation of genetic algorithms

This article tries to connect two separate strands of literature concerning genetic algorithms. On the one hand, extensive research took place in mathematics and closely related sciences in order to find out more about the properties of genetic algorithms as stochastic processes. On the other hand, recent economic literature uses genetic algorithms as a metaphor for social learning. This paper will face the question of what an economist can learn from the mathematical branch of research, especially concerning the convergence and stability properties of the genetic algorithm. It is shown that genetic algorithm learning is a compound of three different learning schemes. First, each particular scheme is analyzed. Then it is shown that it is the combination of the three schemes that gives genetic algorithm learning its special flair: A kind of stability somewhere in between asymptotic convergence and explosion.     

The evolutionary and non-Darwinian economics of Joseph Schumpeter

In a recent paper, Matthias Kelm (1997) accepts that `Schumpeter's definition of evolution does not contain any Darwinian mechanism such as natural selection or any other biological concept' and that Schumpeter `made no such attempt' to apply `Darwinian theory to economic evolution'. However, Kelm goes on to argue that Schumpeter would have been a Darwinian if circumstances were different. It is argued here that this contention is highly implausible because Schumpeter explicitly rejected biological metaphors and analogies in economics. Furthermore, Schumpeter misunderstood Darwinism. In his attempt to `interpret' Schumpeter as a Darwinian, Kelm himself misrepresents the three core principles of Darwinism. In addition Kelm's paper contains several misunderstandings and misrepresentations of the assessment of Schumpeter made by Hodgson (1993). This present response concludes that Schumpeter was indeed one of the greatest economists of the twentieth century and that he may legitimately be described as an `evolutionary economist'. However, he cautioned strongly against the use of biological metaphors in economics and there is no legitimate basis for describing his approach as Darwinian.     

On evolutionary technological change and economic growth: Lakatos as a starting point for appraisal

This paper proposes a discussion on evolutionary technological change and economic growth theory, using the Lakatosian Methodology of Scientific Research Programmes as an appraisal criterion. Since the persistence of some inflexibility in this approach made it difficult to capture fundamental features of the scientific undertaking at hand, an alternative hypothesis was explored, that developed by Hoover (Scientific research program or tribe? A joint appraisal of Lakatos and the new classical macroeconomics. In: de Marchi N, Blaug M (eds) Appraising economic theories: studies in the methodology of research programmes. Edward Elgar, Aldershot, 1991). This latter framework is used here not as a formal methodology but rather as a language to find patterns in these theories. This exercise evolved then towards a number of considerations on the confrontation between these evolutionary theories particularly in terms of that which can be seen (in a loose sense) as their “rival research programme”, the new neoclassical growth models.     

On the geography of conventions

Summary. We study an evolutionary model in which heterogenous boundedly rational agents interact locally in order to play a coordination game. Agents differ in their mobility with mobile agents being able to relocate within a country. We find that mobile agents enjoy a higher payoff and always benefit from increased mobility, while immobile agents benefit from increased mobility at low levels of mobility only. This wedge in payoffs weakly increases as mobility increases. Some extensions are discussed. Received: January 10, 2001; revised version: December 4, 2002 RID="*" ID="*" We thank, without implicating in any way, George Mailath for helpful discussions. Some of the ideas in this paper were developed during the V Conference of the Society for the Advancement of Economic Theory in Ischia, Italy. The NSF provided financial support. Correspondence to: T. Temzelides