Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions

In this paper, a Cournot game with two competing firms is studied. The two competing firms seek the optimality of their quantities by maximizing two different objective functions. The first firm wants to maximize an average of social welfare and profit, while the second firm wants to maximize their relative profit only. We assume that both firms are rational, adopting a bounded rationality mechanism for updating their production outputs. A two-dimensional discrete time map is introduced to analyze the evolution of the game. The map has four equilibrium points and their stability conditions are investigated. We prove the Nash equilibrium point can be destabilized through flip bifurcation only. The obtained results show that the manifold of the game’s map can be analyzed through a one-dimensional map whose analytical form is similar to the well-known logistic map. The critical curves investigations show that the phase plane of game’s map is divided into three zones and, therefore, the map is not invertible. Finally, the contact bifurcation phenomena are discussed using simulation.

The Complexity of Investment Spillover from New-Type Agricultural Business Entities to Small-Scale Farmers

Aiming to clarify the leading roles of new-type agricultural business entities (abbreviated as NABEs) to small-scale farmers, integrated game models between NABEs and small-scale farmers are designed to verify the impact of scale economy and investment spillover on the equilibrium points of the game system. The influence of the investment spillover rate and the decision-making adjustment speed on the stability of the system are emphatically discussed. Numerical simulation shows that, with the increase of small-scale farmers’ decision-making adjustment speed, the system would successively show the phenomena of stability, period doubling bifurcation, chaos and discreteness. In the Cournot game, the two sides’ decision-making results such as investment intensity, selling price and eventual profits vary in the opposite direction. In the Stackelberg game of the basic mode, the two sides’ decision-making results are not evidently changed, and NABEs’ investment intensity, selling price and eventual profits are higher than those of small-scale farmers. In the order mode, system improvement can be realized by controlling the investment spillover rate. The research results indicate that with the increase of the adjustment speed of small-scale farmers’ decision-making, the repeated game decision-making aggravates the instability of the Cournot game system. This paper finds that the order pattern can make up for the scale weakness of small-scale farmers, and finally achieve a win-win situation for decision makers in the case of uncertain demands.

Stackelberg Game Theory for Rectifying Mutual Interferences among Secondary Users of Cognitive Radio Network in Comparison with Cournot Game Theory

Aim: The aim of the study is to solve the problem of mutual interference among SUs based on Stackelberg game theory. Materials and Methods: This paper proposes an innovative algorithm based on Stackelberg game theory to reduce interference among secondary users. MATLAB software is used to implement the algorithm. The algorithm is tested to find Signal to Interference noise ratio (SINR) of about 10 secondary users in CRN using novel Stackelberg game theory and compared with the SINR of Secondary users using Cournot game theory. Results: The Statistical analysis is done by performing Independent Variable test and T-test using SPSS software. The mean SINR is maximum for Stackelberg game theory (100.9±1 mdb), and the least SINR (13.11±1mdb) is seen for Cournot game theory. Conclusion: The algorithm based on Stackelberg game theory shows maximum SINR than the Cournot game theory. Since SINR is maximum Signal quality will be high and Interference will be less among the users due to which the network performance is improved.

On Market Concentration and Disclosure

Verrecchia (1983,1990) introduced the proprietary cost hypothesis in which exogenous disclosure costs are a reduced-form interpretation of lost competitive advantage in product markets. We develop a micro-foundation for this disclosure cost in a Cournot game and explicitly derive the cost as a function of market structure. When the market is sufficiently competitive, this model has a reduced-form representation similar to a standard voluntary disclosure game with a partial disclosure equilibrium. Proprietary costs are increasing in the number of competitors, the degree of product substitution, overall uncertainty and production costs. The analysis also offers new empirical predictions on the interaction between disclosure choice, managerial horizon and entry.

A price discrimination based Cournot game model for high-speed rail and airline

This study investigates the competitive game between high-speed rail and airline on price, profit and social welfare, taking into account the airline price discrimination. We build a multi-level price competition pricing Cournot model for high-speed rail and airline to shed light on the HSR-air transport competition impact of pricing discrimination when airline could offer multi-level class seats, and analyze the optimal pricing strategy of airlines and high-speed rail operators and their impact on social welfare. The analytical results demonstrate that: airline price dis-crimination will increase social welfare and reduce consumer surplus, both airfare and airline profit increase as the degree of price discrimination increases welfare. However, HSR fare and profit decreases with the increase of the degree of price discrimination.

Remanufacturing Mode Selection regarding Technology Development

We consider a Cournot game model between an OEM (original equipment manufacturer) and an IR (independent remanufacturer). The OEM manufactures new products and decides the quality level. IR remanufactures and obtains OEM’s technology through technology licensing or joint R&D. To prevent the cannibalization of new products by remanufactured products, the OEM may be reluctant to disclose latest technology to the IR. When the IR chooses the technology licensing mechanism, it will be in a rather disadvantaged position in the competition. In contrast, joint R&D can avoid this dilemma. The two mechanisms are comparatively analyzed under static equilibrium and complex dynamics from three aspects: (1) the output of new and remanufactured products, (2) the profits of the OEM and the IR, and (3) TEI (total environmental impact) under technology licensing mechanism and joint R&D mechanism, respectively. Based on the theoretical and numerical analysis, we derive that the joint R&D mechanism can achieve a Pareto improvement over the royalty mechanism under certain conditions. The stability, bifurcation, chaos, and largest Lyapunov exponent are analyzed in the dynamic model. Numerical examples show that chaos may cause the OEM and the IR to lose profits or even be in deficit. But from the perspective of TEI, chaos can be beneficial. Interestingly, some conclusions in the static setting are reversed in the chaotic state. We propose a feedback adjustment method to eliminate chaos.

A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers

Many works studied on complex dynamics of Cournot or Stackelberg games, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase. Under the assumption that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Stackelberg–Cournot game with heterogeneous expectations is considered in this paper. Two firms with different R&D capabilities determine their R&D investments sequentially in the Stackelberg R&D phase and make output decisions simultaneously in the Cournot production phase. R&D spillovers, R&D investments, and technological innovation efficiency are introduced in our model. We find that: (i) the boundary equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is unstable if the Nash equilibrium of the system is strictly positive. (ii) The Nash equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is locally asymptotically stable only if the model parameters meet certain conditions. Especially, results indicate that small value of R&D spillovers or big value of output adjustment speed may yield bifurcations or even chaos. Numerical simulations are performed to exhibit maximum Lyapunov exponents, bifurcation diagrams, strange attractors, and sensitive dependence on initial conditions to verify our findings. It is also shown that the chaotic behaviors can be controlled with the state variables feedback and parameter variation method.