Wealth-driven Selection in a Financial Market with Heterogeneous Agents

We study the co-evolution of asset prices and individual wealth in a financial market populated by an arbitrary number of heterogeneous boundedly rational investors. Using wealth dynamics as a selection device we are able to characterize the long run market outcomes, i.e. asset returns and wealth distributions, for a general class of investment behaviors. Our investigation illustrates that market interaction and wealth dynamics pose certain limits on the outcome of agents' interactions even within the ``wilderness of bounded rationality''. As an application we consider the case of heterogenous mean-variance optimizers and provide insights into the results of the simulation model introduced in Levy, Levy and Solomon (1994).Heterogeneous agents, Asset pricing model, Bounded rationality, CRRA framework, Levy-Levy-Solomon model, Evolutionary Finance.

An evolutionary model of firms location with technological externalities

In an economic geography model where both a negative pecuniary and a positive technological externality are present, we introduce an explicit dynamics of firms locational choice and we characterize its long run distribution. Our analysis shows that economic activities evenly distribute when the pecuniary externalities prevail, and agglomerate otherwise. Due to the stochastic nature of the dynamics, even when agglomeration occurs, it is only a metastable state. By giving time and firms heterogeneity a role, we are bringing the evolutionary approach inside the domain of economic geography.Evolutionary Economic Geography; Heterogeneity; Agglomeration; Technological externalities; Markov Chains

A class of evolutionary models for participation games with negative feedback

We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation game with negative feedback. We assume that agents use different behavioral rules prescribing how to play the game conditionally on the outcome of previous rounds. We update the fraction of the population using each rule by means of a general class of evolutionary dynamics based on imitation, which contains both replicator and logit dynamics. Our model is analyzed by a combination of formal analysis and numerical simulations and is able to replicate results from the experimental and computational literature on these types of games. In particular, irrespective of the specific evolutionary dynamics and of the exact behavioral rules used, the dynamics of the aggregate participation rate is consistent with the symmetric mixed strategy Nash equilibrium, whereas individual behavior clearly departs from it. Moreover, as the number of players or speed of adjustment increase the evolutionary dynamics typically becomes unstable and leads to endogenous fluctuations around the steady state. These fluctuations are robust with respect to behavioral rules that try to exploit them.Participation games, Heterogeneous behavioral rules, Revision protocol, Replicator Dynamics Logit Dynamics, Nonlinear dynamics

Informational differences and learning in an asset market with boundedly rational agents

The price formation mechanism in an asset market with boundedly rational agents can be viewed as a filter acting on incoming news about economic fundamentals such as future dividends. Here we study the properties of an asset pricing market filter obtained under some simple behavioral assumptions, and examine the resulting dynamical structure of the fluctuations of the market price around the time-varying underlying fundamental reference price. The starting point is an asset pricing model in which agents can choose among two different degrees of information on fundamentals. At the same time agents are also learning the growth rate of the dividend generating process. This leads to prices that deviate substantially and persistently from the fundamental value in the short run but stay close to it in the long run. In particular, prices follow a time-varying nonlinear mean reverting dynamics which we show to be related to agents' interaction triggered by informational differences.

A class of evolutionary model for participation games with negative feedback (revised version of WP 06-10)

We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation game with negative feedback. We assume that agents use different behavioral rules prescribing how to play the game conditionally on the outcome of previous rounds. We update the fraction of the population using each rule by means of a general class of evolutionary dynamics based on imitation, which contains both replicator and logit dynamics. Our model is analyzed by a combination of formal analysis and numerical simulations and is able to replicate results from the experimental and computational literature on these types of games. In particular, irrespective of the specific evolutionary dynamics and of the exact behavioral rules used, the dynamics of the aggregate participation rate is consistent with the symmetric mixed strategy Nash equilibrium, whereas individual behavior clearly departs from it. Moreover, as the number of players increases the evolutionary dynamics typically becomes unstable and leads to endogenous fluctuations around the steady state. These fluctuations are robust with respect to behavioral rules that try to exploit them.

Selection in asset markets: the good, the bad, and the unknown

In this paper, we use a series of simple examples to illustrate how wealth-driven selection works in a market for Arrow securities. Our analysis delivers both a good and a bad message. The good message is that, when traders invest constant fractions of their wealth in each asset and have equal consumption rates, markets are informationally effcient: the best informed agent is rewarded and asset prices eventually reflect this information. However, and this is the bad message, when asset demands are not constant fractions of wealth but dependent upon prices, markets might behave suboptimally. In this case, asymptotic prices depend on preferences and beliefs of the whole ecology of traders and do not, in general, reflect the best available information. We show that the key difference between the two cases lies in the local, i.e. price dependent, versus global nature of wealth-driven selection.Market Selection; Evolutionary Finance;Informational Efficiency; Asset Pricing; CRRA Preferences

Evolution and market behavior with endogenous investment rules

In a repeated market for short-lived assets, we investigate long run wealth-driven selection on the general class of investment rules that depend on endogenously determined current and past prices. We study the random dynamical system that describes the price and wealth dynamics and characterize local stability of long-run market equilibria. Instability, leading to asset mis-pricing and informational inefficiencies, turns out to be a common phenomenon generated by two different mechanisms. Firstly, conditioning investment decisions on asset prices implies that dominance of an investment rule on others, as measured by the relative entropy, can be different at different prevailing prices thus reducing the global selective capability of the market. Secondly, the feedback existing between past realized prices and current investment decisions can lead to a form of deterministic overshooting.Market Selection; Evolutionary Finance; Price Feedbacks; Asset Pricing; Informational Efficiency; Kelly rule.

A new host record for Euthera fascipennis (Diptera: Tachinidae)

Dolycoris baccarum (Linnaeus) (Heteroptera: Pentatomidae) is reported for the first time as a host of Euthera fascipennis (Loew) (Diptera: Tachinidae). A single specimen of E. fascipennis was reared from an adult of D. baccarum collected in northern Italy (Crevalcore, Bologna, Emilia Romagna Region). This is the first host record for E. fascipennis in Italy and the first distributional record of this tachinid in northern Italy

Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont.

Brock and Hommes (1997) introduce the concept of adaptive rational equilibrium dynamics (ARED)}, where agents choose between a costly rational expectation forecast and a cheap naive forecast, and the fractions using each of the two strategies evolve over time and are endogenously coupled to the market equilibrium price dynamics. In their setting agents are backward looking in the sense that strategy selection is based on experience measured by relative past realized profits. When the selection pressure to switch to the more profitable strategy is high, instability and complicated chaotic price fluctuations arise. In this paper we investigate the ARED with \textit{forward looking} agents, whose strategy selection is based upon expected profits. Our findings suggest that forward looking behavior dampens the amplitude of price fluctuations, but local instability of the steady state remains. The global dynamics depends upon how sophisticated the forward looking behavior is. With perfectly forward looking agents prices converge to a stable 2-cycle, while with forward looking agents who are boundedly rational concerning their estimate of expected profits, small amplitude chaotic price fluctuations may arise. We also establish an equivalence relationship between a heterogeneous agent model with switching of strategies and a representative agent framework, where the representative agent optimally chooses between the benefits of a high quality forecasts and the associated information gathering costs. To an outside observer it is impossible to distinguish between the two.