William R. Parke |
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Research
Recently, I have taken an interest in how evolutionary game theory might provide explanations for the challenges posed by heterogeneous expectations.
An Evolutionary Route to Rational Expectations, with George Waters, July 28, 2008.
Evolutionary game theory provides a fresh perspective on the prospects that agents with heterogeneous expectations might eventually come to agree on a single expectation. We establish conditions under which convergence of beliefs could occur, but also show that persistent heterogeneous expectations can arise if those conditions do not hold. The critical element is the degree of curvature in payoff weighting functions agents use to value forecasting performance. We illustrate our results in the context of an asset pricing model where a martingale solution competes with the fundamental solution for agents’ attention.
While ARCH/GARCH equations have been widely used to model financial market data, formal explanations for the sources of conditional volatility are scarce. This paper presents a model with the property that standard econometric tests detect ARCH/GARCH effects similar to those found in asset returns. We use evolutionary game theory to describe how agents endogenously switch among different forecasting strategies. The agents evaluate past forecast errors in the context of an optimizing model of asset pricing given heterogeneous agents. We show that the prospects for divergent expectations depend on the relative variances of fundamental and extraneous variables and on how aggressively agents are pursuing the optimal forecast. Divergent expectations are the driving force leading to the appearance of ARCH/GARCH in the data.