Wealth-Driven Competition in a Speculative Financial Market: Examples With Maximizing Agents

This paper demonstrates how both quantitative and qualitative results of a general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk aversion assumption can be applied to the special cases of optimizing behavior. The analysis of the asymptotic properties of the market is performed using a geometric approach which allows the visualization of all possible equilibria by means of a simple one-dimensional Equilibrium Market Curve. The case of linear (particularly, mean-variance) investment functions is thoroughly analyzed. This analysis highlights the features which are specific to the linear investment functions. As a consequence, some previous contributions of the agent-based literature are generalized.

Price and Wealth Dynamics in a Speculative Market with Generic Procedurally Rational Traders

An agent-based model of a simple financial market with arbitrary number of traders having relatively general behavioral specifications is analyzed. In a pure exchange economy with two assets, riskless and risky, trading takes place in discrete time under endogenous price formation setting. Traders' demands for the risky asset are expressed as fractions of their individual wealths, so that the dynamical system in terms of wealth and return is obtained. Agents' choices, i.e. investment fractions, are described by means of the generic smooth functions of an infinite information set. The choices can be consistent with (but not limited to) the solutions of the expected utility maximization problems. A complete characterization of equilibria is given. It is shown that irrespectively of the number of agents and of their behavior, all possible equilibria belong to a one-dimensional "Equilibrium Market Line". This geometric tool helps to illustrate possibility of different phenomena, like multiple equilibria, and also can be used for comparative static analysis. The stability conditions of equilibria are derived for general model specification and allow to discuss the relative performances of different strategies and the selection principle governing market dynamics.

Asset Prices, Traders' Behavior, and Market Design

The dynamics in a financial market with heterogeneous agents is analyzed under different market architectures. We start with a tractable behavioral model under Walrasian market clearing and simulate it under more realistic trading protocols. The key behavioral feature of the model is the switching of agents between simple forecasting rules on the basis of fitness measure. Analyzing the dynamics under order-driven protocols we show that behavioral and structural assumptions of the model are closely intertwined. High responsiveness of agents to a fitness measure causes excess volatility, however the frictions of the order-driven markets may stabilize the dynamics.

Evolution of Market Heuristics

The time evolution of aggregate economic variables, such as stock prices, is affected by market expectations of individual investors. Neo-classical economic theory assumes that individuals form expectations rationally, thus enforcing prices to track economic fundamentals and leading to an efficient allocation of resources. However, laboratory experiments with human subjects have shown that individuals do not behave fully rational but instead follow simple heuristics. In laboratory markets prices may show persistent deviations from fundamentals similar to the large swings observed in real stock prices. Here we show that evolutionary selection among simple forecasting heuristics can explain coordination of individual behavior leading to three different aggregate outcomes observed in recent laboratory market forecasting experiments: slow monotonic price convergence, oscillatory dampened price fluctuations and persistent price oscillations. In our model forecasting strategies are selected every period from a small population of plausible heuristics, such as adaptive expectations and trend following rules. Individuals adapt their strategies over time, based on the relative forecasting performance of the heuristics. As a result, the evolutionary switching mechanism exhibits path dependence and matches individual forecasting behavior as well as aggregate market outcomes in the experiments. Our results are in line with recent work on agent-based models of interaction and contribute to a behavioral explanation of universal features of financial markets.

Evolutionary Selection of Individual Expectations and Aggregate Outcomes

In recent 'learning to forecast' experiments with human subjects (Hommes, et al. 2005), three different patterns in aggregate asset price behavior have been observed: slow monotonic convergence, permanent oscillations and dampened fluctuations. We construct a simple model of individual learning, based on performance based evolutionary selectionor reinforcement learning among heterogeneous expectations rules, explaining these different aggregate outcomes. Out-of-sample predictive power of our switching model is higher compared to the rational or other homogeneous expectations benchmarks. Our results show that heterogeneity in expectations is crucial to describe individual forecasting behavior as well as aggregate price behavior.

Evolutionary Selection of Expectations in Positive and Negative Feedback Markets

An economic environment is a feedback system, where dynamics of aggregate variables depend on individual expectations and also shape them. The type of feedback mechanism is crucial for the aggregate outcome. Experiments with human subjects (Heemeijer et al, 2009) have shown that price converges to the fundamental level in the negative feedback environment but fails to do so under positive feedback. We present an explanation of these experimental results by means of a model of evolutionary switching between heuristics. Active heuristics are chosen endogenously, on the basis of their past performance. Under negative feedback an adaptive heuristic dominates explaining fast price convergence, whereas under positive feedback a trend-following heuristic dominates resulting in persistent price deviation and oscillations.

Efficiency of Continuous Double Auctions under Individual Evolutionary Learning with Full or Limited Information

In this paper we explore how specific aspects of market transparency and agents' behavior affect the efficiency of the market outcome. In particular, we are interested whether learning behavior with and without information about actions of other participants improves market efficiency. We consider a simple market for a homogeneous good populated by buyers and sellers. The valuations of the buyers and the costs of the sellers are given exogenously. Agents are involved in consecutive trading sessions, which are organized as a continuous double auction with electronic book. Using Individual Evolutionary Learning agents submit price bids and offers, trying to learn the most profitable strategy by looking at their realized and counterfactual or "foregone" payoffs. We find that learning outcomes heavily depend on information treatments. Under full information about actions of others, agents' orders tend to be similar, while under limited information agents tend to submit their valuations/costs. This behavioral outcome results in higher price volatility for the latter treatment. We also find that learning improves allocative efficiency when compared with to outcomes with Zero-Intelligent traders.

Interest Rate Rules with Heterogeneous Expectations

Recent macroeconomic literature stressed the importance of expectations heterogeneity in the formulation of monetary policy. We use a stylized macro model of Howitt (1992) to investigate the dynamical consequences of alternative interest rate rules when agents have heterogeneous expectations and update their beliefs over time along the lines of Brock and Hommes (1997). We find that the outcome of different monetary policies in terms of stability crucially depends on the ecology of forecasting rules and on the intensity of choice among different predictors. We also show that, when agents have heterogeneous expectations, an interest rate rule that obeys the Taylor principle does not always lead the system to converge to the rational expectations equilibrium but multiple equilibria may persist.

Evolution of market heuristics

Abstract The time evolution of aggregate economic variables, such as stock prices, is affected by market expectations of individual investors. Neoclassical economic theory assumes that individuals form expectations rationally, thus forcing prices to track economic fundamentals and leading to an efficient allocation of resources. However, laboratory experiments with human subjects have shown that individuals do not behave fully rationally but instead follow simple heuristics. In laboratory markets, prices may show persistent deviations from fundamentals similar to the large swings observed in real stock prices. Here we show that evolutionary selection among simple forecasting heuristics can explain coordination of individual behavior, leading to three different aggregate outcomes observed in recent laboratory market-forecasting experiments: slow monotonic price convergence, oscillatory dampened price fluctuations, and persistent price oscillations. In our model, forecasting strategies are selected every period from a small population of plausible heuristics, such as adaptive expectations and trend-following rules. Individuals adapt their strategies over time, based on the relative forecasting performance of the heuristics. As a result, the evolutionary switching mechanism exhibits path dependence and matches individual forecasting behavior as well as aggregate market outcomes in the experiments. Our results are in line with recent work on agent-based models of interaction and contribute to a behavioral explanation of universal features of financial markets. Copyright © Cambridge University Press 2012