Rational vs. irrational beliefs in a complex world

Can boundedly rational agents survive competition with fully rational agents? The authors develop a highly nonlinear heterogeneous agents model with rational forward looking versus boundedly rational backward looking agents and evolving market shares depending on their relative performance. Their novel numerical solution method detects equilibrium paths characterized by complex bubble and crash dynamics. Boundedly rational trend-extrapolators amplify small deviations from fundamentals, while rational agents anticipate market crashes after large bubbles and drive prices back close to fundamental value. Overall rational and non-rational beliefs co-evolve over time, with time-varying impact, and their interaction produces complex endogenous bubble and crashes, without any exogenous shocks.