Relative Profit Maximization Research Articles

Global dynamics of a quantum Cournot duopoly with quadratic costs and relative profit maximization

Global dynamics of a quantum Cournot duopoly with quadratic costs and relative profit maximization

Complexity and chaos control in a Cournot duopoly model based on bounded rationality and relative profit maximization

Complexity and chaos control in a Cournot duopoly model based on bounded rationality and relative profit maximization

Nonlinear Dynamics of a Quantum Cournot Duopoly with Bounded Rationality and Relative Profit Maximization

Based on boundary rationality and relative profit maximization, quantum game theory is applied to develop a dynamic model of the quantum Cournot duopoly game. We investigate the effect of quantum properties on game stability and nonlinear dynamics. The results show that quantum entanglement can improve the model’s stability and control the generation of bifurcation and chaos when comparing the classical game and the game without considering relative profit maximization. It facilitates the player’s choice of quantum entanglement to control the chaos that emerges in the production output. Numerical simulations verify the chaotic properties of the game by means of bifurcations, maximum Lyapunov exponents, and phase diagrams. The results show that quantum entanglement has different effects on different games.

Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

A dynamic Cournot duopoly model with isoelastic demand function and knowledge spillover effects is established, in which the goals of two enterprises are relative profit maximization. Since these two enterprises only have incomplete information of the market, then it is assumed that the enterprises are boundedly rational, and they need to adjust their production decision in next period according to the gradient adjustment mechanism. Sufficient conditions for the existence and stable properties of unique Nash equilibrium can be judged with the help of the Jury criterion. The size of stability region is related to the values of parameters and the system has two different paths to chaos, one is via flip bifurcation and another is via Neimark-Sacker bifurcation. Finally, the complex dynamic characteristics also can be further studied by using numerical simulation, including the structures of multi-layer Arnold's tongues and coexistence of attractors.

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

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

基于相对利润最大化的混合寡头博弈的复杂动态性

基于相对利润最大化的混合寡头博弈的复杂动态性

Research on a Cournot–Bertrand Game Model with Relative Profit Maximization

This paper considers a Cournot–Bertrand game model based on the relative profit maximization with bounded rational players. The existence and stability of the Nash equilibrium of the dynamic model are investigated. The influence of product differentiation degree and the adjustment speed on the stability of the dynamic system is discussed. Furthermore, some complex properties and global stability of the dynamic system are explored. The results find that the higher degree of product differentiation enlarges the stable range of the dynamic system, while the higher unit product cost decreases the stable range of price adjustment and increases the one of output adjustment; period cycles and aperiodic oscillation (quasi-period and chaos) occur via period-doubling or Neimark–Sacker bifurcation, and the attraction domain shrinks with the increase of adjustment speed values. By selecting appropriate control parameters, the chaotic system can return to the stable state. The research of this paper is of great significance to the decision-makers’ price decision and quantity decision.

Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Cost Functions based on Relative Profit Maximization

This paper tries to investigate the complex characteristics behind quantity competition using generalized relative profit functions. For this purpose, we study the dynamics of a nonlinear Cournot – type duopoly game with differentiated goods and generalized relative profit maximization. We suppose a linear demand and asymmetric cost functions. The game is modeled with a system of two difference equations. Results concerning the equilibria of the economic model and their stability are presented and the occurrence of bifurcations is stated. We show that the model gives more complex, chaotic and unpredictable trajectories. Numerical experiments are presented.

Dynamic investigations in a duopoly game with price competition based on relative profit and profit maximization

This paper introduces an attempt to investigate the complex dynamics of a nonlinear duopoly game of players (firms) adopting prices as their decision variables. Two different models are introduced and studied in this paper. The models are built by following the traditional role in which players have limited information. The first model describes a competition between two firms whose main interest is to maximize their relative profits while the second is the classic Bertrand one with profit maximization. The paper shows several local and global analysis about the equilibrium points of each model. We show that classical Bertrand game studied in the second model gives better results than those obtained for the first one however the equilibrium in both models loses its stability via flip bifurcation only.

Equivalence of Cournot and Bertrand equilibria in duopoly under relative profit maximization: A general analysis

Abstract. We study the relationship between Cournot equilibrium and Bertrand equilibrium in duopoly with differentiated goods in which each firm maximizes its relative profit. We show that Cournot equilibrium and Bertrand equilibrium coincide under relative profit maximization even with general demand and cost functions. This result is due to the fact that a game of relative profit maximization in duopoly is a two-person zero-sum game. Keywords. Relative profit maximization, Duopoly, Cournot equilibrium, Bertrand equilibrium. JEL. D43, L13.

Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization

The dynamics of a Cournot duopoly with relative profits maximizations and costs function with externalities is considered. Results concerning the equilibria of the economic model and their stability are presented and the occurrence of bifurcations is stated. A double route to chaotic dynamics, via flip bifurcations and via Neimark–Sacker bifurcations for game is studied. Numerical experiments are presented.

Relative Profit Maximization and Bertrand Equilibrium with Convex Cost Functions

Abstract This study derives pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions and seek to maximize the weighted sum of their absolute and relative profits. The study shows that there exists a range of equilibrium prices in duopolistic equilibria. This range of equilibrium prices is narrower and lower than the range of equilibrium prices in duopolistic equilibria under pure absolute profit maximization. Moreover, the larger the weight on the relative profit, the narrower and lower the range of equilibrium prices. In this sense, relative profit maximization is more aggressive than absolute profit maximization.

Price versus quantity in a mixed duopoly: The case of relative profit maximization

This paper examines the endogenous choice problem of each firm's price or quantity contract in a mixed duopoly composed of one social welfare maximizing public firm and one relative profit-maximizing private firm. In this paper, we show that unless the degree of product differentiation and the degree of importance of the private firm's relative performance are low, the quantity competition can analytically become the unique equilibrium market structure on the basis of the dominant strategies of the public firm and the private firm when the degree of importance of firm 1's relative performance is sufficiently high. This result contrasts strikingly with that obtained in a standard mixed duopoly composed of one social welfare-maximizing public firm and one absolute profit maximizing private firm. In addition, even in the area wherein both the degree of product differentiation and the degree of the private firm's relative performance are sufficiently low, through numerical simulations, the quantity competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently high, whereas the price competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently low.

Choice of strategic variables under relative profit maximization in asymmetric oligopoly: non-equivalence of price strategy and quantity strategy

We consider choice of strategic variables under relative profit maximization in an asymmetric oligopoly with differentiated goods such that there are three firms, Firm 2 and 3 have the same cost function, but Firm 1 has a different cost function. We show that there are two pure strategy sub-game perfect equilibria. 1) All firms choose the outputs as their strategic variables, 2)Firm 2 and 3 choose the outputs as their strategic variables, and Firm 1 chooses the price as its strategic variable.

Relative profit maximization and Bertrand equilibrium with quadratic cost functions

We study the Bertrand equilibrium in duopoly in which two firms produce a homogeneous good under quadratic cost functions, and they seek to maximize the weighted sum of their absolute and relative profits. We show that there exists a range of the equilibrium prices in duopolistic equilibria. This range of equilibrium prices is narrower and lower than the range of the equilibrium prices in duopolistic equilibria under pure absolute profit maximization, and the larger the weight on the relative profit, the narrower and lower the range of the equilibrium prices. In this sense relative profit maximization is more aggressive than absolute profit maximization.

Irrelevance of the choice of strategic variables in duopoly under relative profit maximization

We study the choice of strategic variables by firms in a duopoly in which two firms produce differentiated substitutable goods and each firm maximizes its relative profit that is the difference between its profit and the profit of the rival firm. We consider a two stage game such that in the first stage the firms choose their strategic variables and in the second stage they determine the values of their strategic variables. We show that when the firms maximize their relative profits, the choice of strategic variables is irrelevant to the outcome of the game in the sense that the equilibrium outputs, prices and profits of the firms are the same in all situations, and so any combination of strategy choice by the firms constitutes a sub-game perfect equilibrium in the two stage game. We assume that demand functions for the goods are symmetric and linear, the marginal costs of the firms are common and constant, and the fixed costs are zero.