Search Results (5)

Under the “Dual Carbon” strategy, collaborative governance of port atmospheric pollutants and carbon emissions is critical for low-carbon transformation. Focusing on Ningbo-Zhoushan Port (48% regional ship emissions), this study examines government, port enterprises, and public interactions. A tripartite evolutionary game model with numerical simulation reveals dynamic patterns and key factors. The results show the following: (1) A substitution effect exists between government incentive costs and penalty intensity—increased environmental governance budgets reduce the probability of government incentives, whereas higher public reporting rewards accelerate corporate emission reduction convergence. (2) Public supervision exhibits cyclical fluctuations due to conflicts between individual rationality and collective interests, with excessive reporting rewards potentially triggering free-rider behavior. (3) The system exhibits two stable equilibria: a low-efficiency equilibrium (0,0,0) and a high-efficiency equilibrium (1,1,1). The latter requires policy cost compensation, corporate emission reduction gains exceeding investments, and a supervision benefit–cost ratio greater than 1. Accordingly, the study proposes a three-dimensional “Incentive–Constraint–Collaboration” governance strategy, recommending floating penalty mechanisms, green financial instrument innovation, and community supervision network optimization to balance environmental benefits with fiscal sustainability. This research provides a dynamic decision-making framework for multi-agent collaborative emission reduction in ports, offering both methodological innovation and practical guidance value. Full article

In this research, the intertemporal optimal management of subsidies offered by the environmental regulator and the dynamic conflict between two groups of economic agents involved in environmental quality are discussed. First the environmental model is examined in its optimal control management form with two state variables. The analysis of the improved model, inspecting the social planner’s decision (policy) variable, the variable which influences not only environmental quality but the national budget stock, reveals that is dependent on the growth of the national budget stock. A negative growth rate leads to the long run saddle point equilibrium, while an incremental growth rate, but less than the model’s discount rate, leads to an interesting complicated limit cycle equilibrium, for which under certain parameter values the orbit’s phase portrait can be drawn. For the dynamic game model between the social planner and natural resource exploiters, the equilibrium conditions are examined. It is rather a richer than the point equilibrium for which the cyclical strategies have great importance. Therefore, the conditions for that rich equilibrium are found. As a continuation, the paper concludes that the equilibrium condition is that the players’ discount rates are both greater than the national budget interest rate. Finally, the certain values of the equilibrium strategies and national budget stock are provided. Full article

To effectively understand the collaborative and evolutionary mechanisms of three stakeholders in carbon trading namely, government, emission reduction enterprises, and emission control enterprises, it is important to identify the factors that affect decision-making behaviors amongst game players, ultimately contributing to the goal of “double carbon”. In this study, we constructed a tripartite game model, analyzing the selection mechanism for game strategies related to carbon trading participants through replicated dynamic equations. We also discussed the main factors that influence the evolutionary and stable outcomes of carbon trading through scenario simulations. Additionally, we introduced prospect theory to examine the impact of risk sensitivity and loss avoidance levels amongst decision-makers on the optimal outcome of the system. Our findings reveal that in the initial game model, the three decision-makers show a cyclical behavior pattern, but the system stabilizes in the optimal equilibrium state (1,1,1) when certain conditions are satisfied. Furthermore, the initial willingness of decision-makers impacts the ability of the game system to reach a stable point. Moreover, larger values for the risk sensitivity coefficient and loss avoidance coefficient can promote the evolution of the game system toward an optimal, stable point. Based on these results, targeted countermeasures are proposed to promote activity within the carbon trading market, such as giving more institutional guarantees to carbon trading and stabilizing the carbon price. Full article

This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the interior solution is considered), and the following different tariff schemes are analyzed: linear scheme, increasing block tariff, and convex tariff. Numerical simulations highlight how tariff convexity and seasonality in buyer’s preferences affect water price and demand, and the dynamics of the basin over time. The study shows that synchrony or asynchrony between basin recharge and buyer cyclical demand can dramatically affect the dynamics and basin levels observed at the end of the time period considered. Additionally, the presence of a large number of fluctuations in buyer preferences affects basin fluctuations, while natural recharge may help in maintaining acceptable levels of future water demands. Full article

This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems. Full article