On controlling chaos in a discrete tâtonnement process

The simple pure exchange model with two individuals and two goods by Day and Pianigiani (1991), extensively analyzed by Day (1994, Ch. 10) and taken up again by Mukherjy (1999), is discussed and extended with the purpose of showing that chaos in a discrete tâtonnement process of this kind can be controlled if the auctioneer uses a smooth, nonlinear formulation of the price evolution process such that the price adjustment is a sigmoid-shaped function of the excess demand, with given upper and lower limits. This formulation o¤ers some advantages over previous specifications. In particular, given the speed of adjustment and the excess demand function, we show that, acting on the lower and/or upper limits that constrain price dynamics, the auctioneer can (i) stabilize the dynamics, (ii) reduce the complexity of the attractor and (iii) increase the economic significance of the adjustment process