Chaotic dynamics in Bertrand model with technological innovation

Abstract

Abstract. In this paper, the dynamics of a Bertrand duopoly game with technology innovation have been studied, which contains boundedly rational and naive players. They have been analyzed that the stability of the equilibrium point, the bifurcation and chaotic behavior of the dynamic system. It has been proved that technology innovation has played a very important role in the stability of Nash equilibrium point. Technology innovation can enlarge the stability region of the speed and control the chaos of the dynamic system effectively.

An Empirical Study of a Mathematical Model for Influence of Government Tax on the Price Behavior and the Stability of Market Price

“…We consider a Bertrand-type duopoly market where two oligopolies choose different prices for their heterogeneous products. Players can decide the prices according to the adjustment rules [30]. Hypothesis 1.…”

“…e dynamic duopoly game will achieve a Nash Equilibrium at last. e possible equilibrium point of map ( 8) can be obtained as nonnegative solution of the nonlinear algebraic system [30]:…”

“…In MATLAB programming, given the number of iterations is N � 500, the other parameters are satisfied under (12) conditions. e influence of price adjustment coefficient and government tax ratio on the price behavior of enterprises in market is investigated [30][31][32][33][34].…”

Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

“…Reference [15] includes many in-depth studies on Cournot duopoly games, which have provided important results on the complex dynamics of such games. Using the technical innovation of naive expectations and bounded rationality, the complex dynamics of a Bertrand duopoly game in [16] have been studied.…”

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

“…Askar and Alkhedhairi [6] introduced two different Bertrand duopoly models where the first one is the competition of price in which each player wants to maximize its relative profit, and the second model is the classic Bertrand competition in which the players want to maximize their profits. ere is still some literature which studies the Bertrand game theory and the complexity of the dynamical system; see [7][8][9][10][11][12]. e above price game models assume that firms play simultaneous-move games; however, the competition among oligarchs in the real market is mostly a dynamic game or sequential game.…”