Analysis of a Four‐Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms

Abstract

In this paper, the Caputo derivative with fractional orders is suggested to model a competition among four competing firms. The proposed economic model that describes this competition is constructed based on a generalization of the traditional bounded rationality. In this generalization, we study the influence of memory parameter on the complex behavior of the model. Memory means that we not only take into account the changes in quantities at a current time, but also study the changes occurring in the quantities during an interval of time. For simplicity, it is assumed that the degree of memory is described by one parameter during that interval. The properties of the proposed model such as stability of equilibria, bifurcation, and chaos are studied. Furthermore, we introduce and study the cooperation that may take place among the four firms using Keeney-Raiffa approach.

Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

“…Another Cournot duopoly game with competed players having capacity constraints was considered based on utility function of Cobb-Douglas in Reference [9]. Other studies for Cobb-Douglas and the dynamic analysis for games based on it can be found elsewhere [10][11][12][13][14][15][16]. In Reference [17], the complex dynamic characteristics of a novel nonlinear finance system was investigated.…”

The effect of caputo fractional difference operator on a novel game theory model

“…The Nash equilibria, their local stability and the presence of chaos are deeply investigated [17]. In [5] a discrete dynamic system that describes the competition among four firms is presented. In particular, the fractional bounded rationality is taken into account and the stability of the Nash point is studied [5].…”

“…In [5] a discrete dynamic system that describes the competition among four firms is presented. In particular, the fractional bounded rationality is taken into account and the stability of the Nash point is studied [5]. However, while the fractional duopoly game, where two firms compete over a market, has been studied [19, 2, ?…”

“…Based on the dynamical system (5), we propose a new generalized model by introducing the Caputo-like difference operator on the system. (5). Specifically, our main interest is to study the dynamics of three bounded rationality firms with relative profit maximization and long memory of output decision.…”