Rational vs. Irrational Beliefs in a Complex World

Can boundedly rational agents survive competition with fully rational agents? We develop a highly nonlinear heterogeneous agents model with rational forward looking versus boundedly rational back- ward looking agents and evolving market shares depending on their relative performance. Our novel numerical solution method detects equilibrium paths characterized by complex bubble and crash dy- namics. Boundedly rational trend-extrapolators amplify small deviations from fundamentals, while rational agents anticipate market crashes after large bubbles and drive prices back close to fundamen- tal 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.