Using system dynamics to analyse interactions in duopoly competition

Abstract

This article introduces non‐linear dynamics to assess the interactions in duopoly competition between two rivals. The generic competition is considered here to be the competition for quality between two consumer durable products. The authors have used a system dynamics approach to develop the model of interactions and simulate the behaviour over time. The outcomes of several hundred simulations have shown that the recognition and implementation lags in quality improvement strongly influence the qualitative behaviour of the system. When the speed of adaptation to customer demand reaches a certain value, a Hopf bifurcation occurs and the system converges into a limit cycle. Quasi‐periodicity and chaos emerge when further increasing the speed of the response. Instead of tending to equilibrium around an optimal quality value the model exhibits complex counter‐intuitive behaviours. Copyright © 2000 John Wiley & Sons, Ltd.

Research on the evolutionary game of environmental pollution in system dynamics model

“…Kim and Kim (1997) proposed an SD model for a mixed-strategy game between police and driver and carried out a qualitative analysis on its simulation result. Sice, Mosekilde, Moscardini, Lawler, and French (2000) used an SD approach to develop the model of interactions in duopoly competition between two rivals and simulated the behaviour over time, which showed that the model exhibited complex counter-intuitive behaviours instead of tending to equilibrium around an optimal value. SD will simulate evolutionary processes of games towards (non-)equilibrium states, while game theory provides framework for modelling the world, which is full of both competition and cooperation with all kinds of uncertainties.…”

A study of duopolistic dynamics with competitive advertising based on state-dependent switching behavior

“…It is easy to see that condition (22) will be satisfied if c 11 = c 22 , c 12 = c 21 , k 11 = k 22 . Section V-D will show that (22) predicts the location of the sliding equilibrium exactly, when c 12 is varied (but all equalities are maintained).…”

“…Section V-D will show that (22) predicts the location of the sliding equilibrium exactly, when c 12 is varied (but all equalities are maintained).…”

“…The paper [21] studies different patterns of equilibria without concentrating on the search for any optimal behavior. In [22], the authors exploit the different aspects of the dynamics of a duopolistic model also without a specific focus on optimality. Similarly, our perspective is this paper is to investigate basic patterns of the dynamics of a proposed model submitted to different competitive advertising policies.…”

“…2) for both of which x 1 (0) < x 2 (0). Convergence to the equal market shares is determined by the location of the initial condition.that, although they lie on the equal market share line, are further away from the fair share, full capacity point: this follows analytically from(22), keeping k 11 = k 22 , c 11 = c 22 fixed and varying the predation parameters c 12 = c 21 (but maintaining them equal for both competitors). Model 2: Showing the influence of the predation parameter c 21…”