Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

Abstract

We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.

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

“…Based on Cournot or Bertrand game in oligopolistic market [1][2][3], have studied a lot and reported a large amount of works. With the spillover effect, Zha et al [4] studied the Nash equilibrium stability of Bertrand duopoly game. In [5], the dynamic characteristics of closed-loop Bertrand game have been investigated in supply chain.…”

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.…”

A Bertrand Duopoly Game with Long-Memory Effects

“…ere are many types of games, such as the Cournot game [1][2][3][4][5][6][7], the Bertrand game [8][9][10][11][12][13][14], the Stackelberg game [15][16][17], the evolutionary game [18], and the mixed game [19]. Many researchers have studied duopoly games with some interesting characteristics, such as bounded rationality [1,[15][16][17], technology licensing [3,20], and R&D [6,13]. Table 1 shows some recent research studies on duopoly games with integer-order difference equations.…”