We consider the standard cobweb market where all suppliers share a quadratic cost function and naive price expectations, and the market demand function is isoelastic.

If all suppliers produce the profit-maximizing amount immediately (henceforth 'naive' behavior) and the price elasticity is greater than one, the market is stable and converges to an equilibrium price. If the price elasticity shrinks due to higher advertising expenditures, e.g., and gets smaller than one, the price trajectory becomes unstable and explodes. Suppose that there appears a different-type supplier who adjusts adaptively his/her last period's production in the direction of the production amount that is profit-maximizing under naive expectations (henceforth 'adaptive' behavior). Then the market will not explode but begin to behave chaotically. As the number of adaptive suppliers increases, the amplitude of chaotic behavior of the market becomes smaller. Adaptive behavior stabilizes the cobweb market that is unstable without an adaptive agent. A single adaptive supplier may change the behavior of the market.

On the contrary, if all suppliers behave adaptively, the unstable cobweb market is either in a stable equilibrium, a periodic oscillation or a chaotic situation, depending on the constellation of parameters. In the case of periodic oscillation, there exists the only periodic attractor. If there appears a naive supplier among adaptive ones, then the market may exhibit infinitely many coexisting periodic attractors. A single naive supplier may change the behavior of the market.