Instability in the Cobweb Model Under the BNN Dynamic

Abstract

The cobweb model where firms choose between rational and naive forecasting strategies has a 2-cycle when the slope of supply is greater than the slope of demand for a number of different dynamics describing the evolution of strategy choices. This paper proves that the 2-cycle is exponentially unstable under the learning dynamic of Brown, von Neuman and Nash (1950). Issues arising in the analysis of piecewise smooth discrete time maps are discussed.

Keywords: Chaos, Cobweb Model, Learning, BNN

JEL Classification: C62, C73, D83, D84