The Game Analysis of Price Competition on Different Rationality

Classical model of price competition is based on the supposition of complete rationality, but it´s impossible for this supposition to exist in reality. In the paper, on the supposition of bounded rationality, we construct two Bertrand price competition models :one is based on competitors with complete rationality and the ones with bounded rationality, the other is on two competitors with bounded rationality. We analyze Nash equilibrium and its stability. Through numerical simulation, we show that, in duopoly price competition, two competitors can attain stable Nash equibrium,only to satisfy certain conditions (in stable region), and beyond the stable region, dynamic system has sensitive dependence to the initial value. But, due to limitation of its rationality,the game players with bounded rationality often fall into the disruption of market ( chaotic status) with their eagerness for quick success and instant benefits , and then affect their own long-term strategic interests.