Interacting agents in finance, entry written for the New Palgrave Dictionary of Economics, Second Edition, edited by L. Blume and S. Durlauf, Palgrave Macmillan, forthcoming 2006.

Interacting agents in finance represent a behavioral, agent-based approach in which financial markets are viewed as complex adaptive systems consisting of many boundedly rational agents interacting through simple heterogeneous investment strategies, constantly adapting their behavior in response to new information, strategy performance and through social interactions. An interacting agent system acts as a noise filter, transforming and amplifying purely random news about economic fundamentals into an aggregate market outcome exhibiting important stylized facts such as unpredictable asset prices and returns, excess volatility, temporary bubbles and sudden crashes, large and persistent trading volume, clustered volatility and long memory.

Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164.

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamics. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behaviour occur when agents become more sensitive to differences in evolutionary fitness.

Economic Dynamics, Contribution to the Encyclopedia of Nonlinear Science, Alwyn Scott (ed.), Routledge, 2004.

Contribution to the Encyclopedia of Nonlinear Science, Alwyn Scott (ed.), Routledge, 2005, pp.245-248.

Complexity, Evolution and Learning: a simple story of heterogeneous expectations and some empirical and experimental validation.

This note discusses complexity models in economics. A key feature of these models is that agents have heterogeneous expectations, disciplined by adaptive learning and evolutionary selection. Agents adapt their rules based upon past observations and switch between different forecasting heuristics based upon strategy performance. We discuss how these models match empirical facts as well as laboratory experiments with human subjects and how this approach may tame the ``wilderness of bounded rationality''.

Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006, pp.1109-1186.

This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

Bounded Rationality and Learning in Complex Markets

This chapter reviews some work on bounded rationality, expectation formation and learning in complex markets, using the familiar demand-supply cobweb model. We emphasize two stories of bounded rationality, one story of adaptive learning and another story of evolutionary selection. According to the adaptive learning story agents are identical, and can be represented by an ``average agent'', who adapts his behavior trying to learn an optimal rule within a class of simple (e.g. linear) rules. The second story is concerned with heterogeneous, interacting agents and evolutionary selection of different forecasting rules. Agents can choose between costly sophisticated forecasting strategies, such as rational expectations, and freely available simple strategies, such as naive expectations, based upon their past performance. We also confront both stories to laboratory experiments on expectation formation. At the end of the chapter, we integrate both stories and consider an economy with evolutionary selection between a costly sophisticated adaptive learning rule and a cheap simple forecasting rule such as naive expectations.

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.

Heterogeneous beliefs and and routes to complez dynamics in asset pricing models with price contingent contracts

This paper discusses dynamic evolutionary multi-agent systems, as introduced by Brock and Hommes (1997). In particular the heterogeneous agent dynamic asset pricing model of Brock and Hommes (1998) is extended by introducing derivative securities by means of price contingent contracts. Numerical simulations suggest that in a boundedly rational heterogeneous evolutionary world futures markets may be destabilizing.

Individual Expectations and Aggregate Behavior in Learning to Forcast Experiments

Models with heterogeneous interacting agents explain macro phenomena through interactions at the micro level. We propose genetic algorithms as a model for individual expectations to explain aggregate market phenomena. The model explains all stylized facts observed in aggregate price fluctuations and individual forecasting behaviour in recent learning to forecast laboratory experiments with human subjects (Hommes et al. 2007), simultaneously and across different treatments.

Complex evolutionary systems in behavioral finance

Traditional finance is built on the rationality paradigm. This chapter discusses simple models from an alternative approach in which financial markets are viewed as complex evolutionary systems. Agents are boundedly rational and base their investment decisions upon market forecasting heuristics. Prices and beliefs about future prices co-evolve over time with mutual feedback. Strategy choice is driven by evolutionary selection, so that agents tend to adopt strategies that were successful in the past. Calibration of "simple complexity models" with heterogeneous expectations to real financial market data and laboratory experiments with human subjects are also discussed.