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

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.

Survival in Speculative Markets

In this paper, I consider an exchange economy with complete markets where agents have heterogeneous beliefs and, possibly, preferences, and investigate the Market Selection Hypothesis that speculation rewards the agent with the most accurate beliefs. First, on the methodological level, I derive the relative consumption dynamics as a function of agents’ effective discount factors, related to consumption decisions across time, and agents’ effective beliefs, related to consumption decisions across states. Sufficient conditions for agents’ survival, either in isolation or in a group, depend on the relative size of effective discount factors and on the relative accuracy of effective beliefs. Then, I show that in economies where agents maximize an Epstein-Zin utility the Market Selection Hypothesis fails: there exist parametrizations where the agent with correct beliefs vanishes and parametrizations where beliefs heterogeneity persists in the long run. Results are robust to local changes of beliefs, risk preferences, and the aggregate endowment process. These failures are shown not to occur when agents’ Epstein-Zin utility has a subjective expected utility representation due to an interdependence of effective discount factors and effective beliefs

Equilibrium return and agents' survival in a multiperiod asset market: analytic support of a simulation model

We study the co-evolution of asset prices and agents’ wealth in a financial market populated by an arbitrary number of heterogeneous, boundedly rational investors. We model assets’ demand to be proportional to agents’ wealth, so that wealth dynamics can be used as a selection device. For a general class of investment behaviors, we are able to characterize the long run market outcome, i.e. the steady-state equilibrium values of asset return, and agents’ survival. Our investigation illustrates that market forces pose certain limits on the outcome of agents’ interactions even within the “wilderness of bounded rationality”. As an application we show that our analysis provides a rigorous explanation for the results of the simulation model introduced in Levy, Levy, and Solomon (1994)

The Wisdom of the Crowd in Dynamic Economies

The wisdom of the crowd applied to financial markets asserts that prices represent a consensus belief that is more accurate than individual beliefs. However, a market selection argument implies that prices eventually reflect only the beliefs of the most accurate agent. In this paper, we show how to reconcile these alternative points of view. In markets in which agents naively learn from equilibrium prices, a dynamic wisdom of the crowd holds. Market participation increases agents' accuracy, and equilibrium prices are more accurate than the most accurate agent

Long-run heterogeneity in an exchange economy with fixed-mix traders

We consider an exchange economy where agents have heterogeneous beliefs and assets are long-lived, and investigate the coupled dynamics of asset prices and agentsâ wealth. We assume that agents hold fixed-mix portfolios and invest on each asset proportionally to its expected dividends. We prove the existence and uniqueness of a sequence of arbitrage-free market equilibrium prices and provide sufficient conditions for an agent, or a group of agents, to survive or dominate. Our main finding is that long-run coexistence of agents with heterogeneous beliefs, leading to asset prices endogenous fluctuations, is a generic outcome of the market selection process