Conventions,local interaction,and automata networks

This paper deals with the evolution of conventions in a finite population of boundedly rational players. We apply methods from the theory of automata networks to analyze the effects of different interaction structures. It is shown that the size of the reference group for each player has an important impact on the evolutionary stability of a particular convention, and that the interaction structure crucially determines the distribution of conventions in the population.     

A close eye on the invisible hand

The paper shows how, and under what minimal information supply conditions, a market finds its competitive equilibrium price and thus solves the so-called tatonnement process, without sellers and buyers knowing the equilibrium price in advance. The information premises must be understood as a basic first approach, and do not necessarily mimic the real market process. Demonstration of a discovery process under these information handling conditions is an important finding for an evolutionary market theory. Additional information-processing elements should augment the efficiency of the discovery process. The results of the simulated market process set out above raise new questions. The role of institutional elements (such as the relevance of demand flexibility or “certainty” of knowledge in the learning process, etc.) is discussed further outside the context of the simulation model, providing new insight into the market process.     

Long run equilibria in an asymmetric oligopoly

Summary. Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each group. I will show the following results. 1) The finite population evolutionarily stable strategy (ESS) output is equal to the competitive (or Walrasian) output in each group of the firms. 2) Under the assumption that the marginal cost is increasing, the ESS state is the long run equilibrium in the stochastic evolutionary dynamics in the limit as the output grid step, which will be defined in the paper, approaches to zero. Received: September 19, 1997; revised: June 18, 1998     

Does Neutral Stability Imply Lyapunov Stability?

A central concept in evolutionary game theory is that of an evolutionarily stable strategy. However, many games of interest for economics have only strategies which meet the weaker requirement of neutral stability. While neutral stability implies Lyapunov stability under the replicator dynamics in pairwise interactions, we give here an example in which an evolutionarily stable strategy is not Lyapunov stable in a more general context. We propose to use instead the notions of (strong) uninvadability and (strong) unbeatability, refinements of evolutionary and neutral stability, respectively. Strong uninvadability implies asymptotic stability, and strong unbeatability implies Lyapunov stability under the replicator dynamics. Journal of Economic Literature Classification Number: C72.     

Evolution of harvesting strategies: replicator and resource dynamics

Abstract. Economic theories of managing renewable resources, such as fisheries and forestry, traditionally assume that individual harvesters are perfectly rational and thus able to compute the harvesting strategy that maximizes their discounted profits. The current paper presents an alternative approach based on bounded rationality and evolutionary mechanisms. It is assumed that individual harvesters face a choice between two harvesting strategies. The evolution of the distribution of strategies in the population is modeled through a replicator dynamics equation. The latter captures the idea that strategies yielding above average profits are demanded more than strategies yielding below average profits, so that the first type ends up accounting for a larger part in the population. From a mathematical perspective, the combination of resource and evolutionary processes leads to complex dynamics. The paper presents the existence and stability conditions for each steady-state of the system and analyzes dynamic paths to the equilibrium. In addition, effects of changes in prices are analyzed. A main result of the paper is that under certain conditions both strategies can survive in the long-run. Correspondence to: J. Noailly     

The power of ESS: An experimental study

Abstract. Our experimental design mimics a traditional evolutionary game framework where players are matched pairwise to play a symmetric 33 bimatrix game that has two Nash equilibria. One equilibrium is an evolutionary stable state, or ESS; the other is an equilibrium in dominated strategies. Our primary experimental result is the observation that the ESS becomes extremely attractive when subjects have minimal information about the payoff functions, although the dominated equilibrium assures the highest equilibrium payoff. The attractiveness of the ESS is only moderate when players are completely informed about the 33 payoff matrix. Correspondence to: S.K. Berninghaus     

Evolutionary stability of discrimination under observability

We study the evolution of preferences under perfect and almost perfect observability in symmetric 2-player games. We demonstrate that if nature can choose from a sufficiently general preference space, which includes preferences over outcomes that may depend on the opponent's preference-type, then, in most games, only discriminating preferences (treating different types of opponents differently in the same situation) can be evolutionary stable and some discriminating types are stable in a very strong sense in all games. We use these discriminating types to show that any symmetric outcome which gives players more than their minmax value in material payoffs (fitness) can be seen as equilibrium play of a player population with such strongly stable preferences.     

Evolutionary stability of discrimination under observability

We study the evolution of preferences under perfect and almost perfect observability in symmetric 2-player games. We demonstrate that if nature can choose from a sufficiently general preference space, which includes preferences over outcomes that may depend on the opponent's preference-type, then, in most games, only discriminating preferences (treating different types of opponents differently in the same situation) can be evolutionary stable and some discriminating types are stable in a very strong sense in all games. We use these discriminating types to show that any symmetric outcome which gives players more than their minmax value in material payoffs (fitness) can be seen as equilibrium play of a player population with such strongly stable preferences.     

Localized knowledge percolation processes and information networks

Summary The development of knowledge within industries is strongly influenced by the network structure of relations among firms. Firms relying on localized knowledge can implement their technological capability not only by means of research and development expenditures and internal learning but also through the systematic absorption of technological and scientific externalities available in their environment. Percolation processes have been studied in physics as the outcome of two classes of forces termed as connectivity and receptivity. The former measures the number of connections in place among the agents in the network and the latter the capability of each agent to absorb the informations received. This paper applies the methodology of percolation processes to operationalize the implications for both the economics of innovation and for technology policy of the structural characteristics of innovation networks as communication systems.     

Sophisticated imitation in cyclic games

Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finite sample of other outcomes within their population. Individuals from the same population follow the same behavioral rule. In the resulting discrete time dynamics the unique Nash equilibrium is unstable. However, for sample sizes greater than one, we present an imitation rule where long run play cycles closely around the equilibrium.     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

Optimality and Natural Selection in Markets

We ask if natural selection in markets favors profit-maximizing firms and, if so, is there a difference between the predictions of models which assume all firms are profit maximizers and the predictions of models which explicitly take account of population dynamics in the market. We show that market selection favors profit maximizing firms, but we also show that the long-run behavior of evolutionary market models is nonetheless not consistent with equilibrium models based on the profit-maximization hypothesis. Dynamic equilibrium paths with market selection are not Pareto optimal, nor even asymptotically optimal. The discrepancy arises because the dynamics created by firm evolution causes prices to vary over time and the resulting dynamical system need not have stable steady states.     

When will payoff maximization survive? An indirect evolutionary analysis

Survival of payoff maximization is the usual as if-justification for assuming rational economic agents. An indirect evolutionary analysis allows for stimuli which are not directly related to reproductive success although they affect behavior. One first determines the solution for all possible constellations of stimuli, and then the evolutionarily stable stimuli. Our general analysis confirms the special results of former studies that payoff maximization in case of commonly known stimuli requires either that own success does not depend on other's behavior or that other's behavior is not influenced by own stimuli. When stimuli are private information, one can derive similar necessary conditions.     

Evolutionary equilibrium in Tullock contests: spite and overdissipation

Tullock's analysis of rent-seeking as a contest is reconsidered from an evolutionary point of view. We show that evolutionarily stable behavior in a Tullock contest exists and differs from behavior in Nash equilibrium. Evolutionarily stable behavior in these contests is robust in a strong sense and may entail overdissipation of the contested rent.     

An evolutionary model of the size distribution of firms

An analytical study of the evolution of the distribution of firm size in an industry is presented. A drift-diffusion model is proposed to express the time-evolution of density of firm size within the industry. The model blends the conventional, more or less static, determinants with the kinds of dynamic considerations introduced by stochastic processes of evolutionary dynamics. The steady-state distribution as well as the dynamic behavior of the model are derived. Parameters in the resulting analytical expressions are then fit to a population of firms in the non-manufacturing service sector. The empirical portion of the paper validates the proposed evolutionary model.     

Evolutionary Stability in Alternating-Offers Bargaining Games

This paper characterizes modified evolutionarily stable strategies (messes) in Rubinstein's alternating-offers, infinite-horizon bargaining game. We show that a mess causes agreement to be achieved immediately, with neither player willing to delay the agreement by one period in order to achieve the other player's share of the surplus. Each player's share of the surplus is then bounded between the shares received by the two players in the unique subgame-perfect equilibrium of Rubinstein's game. As the probability of a break-down in negotiations becomes small (or discount factors become large), these bounds collapse on the subgame-perfect equilibrium.Journal of Economic LiteratureClassification Numbers C70, C78.     

On the evolutionary selection of sets of Nash equilibria

It is well established for evolutionary dynamics in asymmetric games that a pure strategy combination is asymptotically stable if and only if it is a strict Nash equilibrium. We use an extension of the notion of a strict Nash equilibrium to sets of strategy combinations called ‘strict equilibrium set’ and show the following. For a large class of evolutionary dynamics, including all monotone regular selection dynamics, every asymptotically stable set of rest points that contains a pure strategy combination in each of its connected components is a strict equilibrium set. A converse statement holds for two-person games, for convex sets and for the standard replicator dynamic.     

Firm survival in the German automobile industry

In this paper, methods of duration analysis are applied to investigate determinants of firm survival in the German automobile industry during the period 1886–1939. A new comprehensive data set has been assembled in order to secure data comparable to that for the US automobile industry. Our results show that the forces shaping the survival pattern of firms over the life cycle are quite similar in both countries, i.e. early entry in the life cycle and prior experience are associated with a lower risk of exit. This finding holds equally when parametric, semiparametric and nonparametric methods are applied.We thank the participants of the 10th conference of the International Schumpeter Society in Milan, June 2004, and the 31st EARIE conference in Berlin, September 2004, for helpful discussion. We also thank two anonymous referees for their comments. All remaining errors are in our responsibility.     

On the Dynamic Foundation of Evolutionary Stability in Continuous Models

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games. Journal of Economic Literature Classification Numbers: C70, 72.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.