Differential Game Models in Transboundary Pollution Control
Summary
Differential game theory provides a dynamic framework for analysing strategic interactions between sovereign regions that share environmental resources or bear cross-border pollution risks. In these models, each region is represented as a decision-maker that controls abatement investments, emission trading or ecological compensation to influence a common pollution stock evolving over time. Two principal paradigms are distinguished: noncooperative games, in which regions optimise individual welfare and often lead to free-riding or border-effect inefficiencies; and cooperative games, which internalise externalities through joint planning, compensation mechanisms or permit trading schemes. Mathematical tools such as Hamilton–Jacobi–Bellman equations and feedback Nash equilibria enable the characterisation of optimal emission paths under stochastic or deterministic pollution dynamics. Extensions incorporate spatial diffusion and advection of contaminants, multiple pollutants, asymmetric endowments and hierarchical leader–follower (Stackelberg) settings. Across air, water and soil contexts, differential game models yield policy insights on the design of transfers, compensation rates and market-based instruments, highlighting conditions under which Pareto improvements are attainable. By capturing both temporal and spatial dimensions of transboundary pollution, this approach informs international negotiation, basin-wide management and climate-related bargaining in a rigorous yet policy-relevant manner.
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Differential Game Models in Transboundary Pollution Control publication trend
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Technical terms
Differential game: A dynamic framework in which multiple decision-makers control state variables over time to optimise individual or collective objectives.
Stackelberg game: A hierarchical model where a leader region moves first, and followers adjust their strategies in response to the leader’s decision.
Feedback Nash equilibrium: A set of state-dependent control rules from which no player can gain by deviating unilaterally given others’ strategies.
Hamilton–Jacobi–Bellman equation: A partial differential equation that characterises the value function of an optimal control or differential game problem.
Ecological compensation: Transfer payments or incentives designed to align upstream and downstream abatement efforts in transboundary contexts.
Spatiotemporal diffusion–advection: Mathematical description of how pollutants spread across space and time under natural transport processes.
References
- Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game. PLOS ONE (2015).
- A Differential Game of Transboundary Pollution Control and Ecological Compensation in a River Basin. Complexity (2020).
- A dynamic theory of spatial externalities. Games and Economic Behavior (2022).
- Dynamic Optimal Control Differential Game of Ecological Compensation for Multipollutant Transboundary Pollution. Complexity (2021).
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