Government supervision and people participation play vital roles in enterprises' green production strategy, but few studies have considered the strategy choices behind government supervision and people's participation. This study contended that whether an enterprise adopts the green production strategy is influenced not only by its responsible attitude facing social responsibility but also by the following two factors, the intensity of government supervision and whether people choose to participate in supervision or not when facing the enterprise adopting the green production strategy or not. We constructed a tripartite evolutionary game model to explore the behavioral evolution rules and evolutionary stability strategies of government supervision, people participation, and enterprises' green production. Then we employed numerical simulation to analyze how various factors influence the strategy selection of the government, people, and enterprises. The results show that if the utility values of government supervision and people participation are greater than 0, the enterprises will adopt the green production strategy. The system stability is affected by a synergistic relationship between participation cost, reputation benefit, and government subsidies, and an incremental relationship between enterprises' green production benefit, government subsidies, people's reported bonus, and enterprises' green production cost. This study provides a new theoretical perspective for research on government supervision, people participation, and enterprises' green production strategy, and the results provide important references for improving the enterprises' green production and urban environmental management.

Purpose: From the quantum game perspective, this paper aims to study a green product optimal pricing problem of the dual-channel supply chain under the cooperation of the retailer and manufacturer to reduce carbon emissions. Design/methodology/approach: The decentralized and centralized decision-making optimal prices and profits are obtained by establishing the classical and quantum game models. Then the classical game and quantum game are compared. Findings: When the quantum entanglement is greater than 0, the selling prices of the quantum model are higher than the classical model. Through theoretical research and numerical analysis results, centralized decision-making is more economical and efficient than decentralized decision-making. Publicity and education on carbon emission reduction for consumers will help consumers accept carbon emission reduction products with slightly higher prices. When the emission reduction increases too fast, the cost of emission reduction will form a significant burden and affect the profits of manufacturers and supply chain systems. Originality/value: From the perspective of the quantum game, the author explores the optimal prices of green product and compares them with the classical game.

The development of quantum information theory based on quantum entangled states is advancing rapidly and has promoted the emergence of quantum game theory. Quantum game theory is quantum information processing applied to classical games, which solves problems that classical games cannot solve. This paper explores the quantum Cournot-Bertrand game model of two firms in a duopoly market with bounded rationality and product substitutability. The first and second firms choose production output and sales price as their decision variables, respectively. We first define the quantum Cournot-Bertrand dynamical system and study the existence and locally stable conditions of equilibrium points. Then we explore bifurcation conditions and bifurcation types. Finally, we do the bifurcation analysis and explore the impacts of the model parameters as the potential market size of products, the two firms' linear marginal cost, the players' speed of strategy adjustment, the product substitution index, and the quantum entanglement degree on the Nash equilibrium stability and bifurcation using numerical analysis and simulation, and provide economic explanations for the results.

Project Euclid - mathematics and statistics online

This paper examines a duopoly market comprising two firms, where the first firm optimizes its output and the second firm optimizes its price. We establish a quantum Cournot-Bertrand dynamical system from the perspective of quantum game theory to study the existence and stability conditions of equilibrium points and conduct bifurcation analysis on equilibrium points. A controlled quantum Cournot-Bertrand dynamical system is also established, which delays, advances, or eliminates the generation of bifurcations and chaos by appropriately selecting model parameter values. Finally, numerical simulation and analysis are conducted to verify the theoretical correctness of the research model and explore the influence of model parameter values on quantum game strategies. We also provide relevant economic explanations in the process. The research results indicate that the potential market size increases will lead to the instability of the quantum strategy. The impact of the two firms’ cost control parameters on their respective quantum strategy is reversed. The second firm’s control parameter of cost continuously decreasing will lead to its quantum strategy entering bifurcations and chaos. The quantum strategy’s sensitivity to the second firm’s marginal cost, strategy adjustment speed, and quantum entanglement degree is higher than that of the first firm’s marginal cost, strategy adjustment speed, and quantum entanglement degree, respectively. The continuous increase of other parameter values will lead to the second firm’s quantum strategy entering bifurcation and chaos, followed by the first firm’s quantum strategy entering bifurcation and chaos.