Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 11, Iss. 3, July, 2007, pp. 367-395
@2007 Society for Chaos Theory in Psychology & Life Sciences

 
 
 

Delayed Nonlinear Cournot and Bertrand Dynamics with Product Differentiation

Akio Matsumoto, Chuo University, Tokyo, Japan
Ferenc Szidarovszky, University of Arizona, Tucson, AZ

Abstract: Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.

Keywords: delayed dynamics, product differentiation, nonlinear duopoly, limit cycle