Abstract
This paper studies a Stackelberg differential game between an upstream region and a downstream region for transboundary pollution control and ecological compensation in a river basin and increases the number of pollutants assumed in the model to multiple. Emission and green innovation investment between upstream and downstream regions in the same basin is a Stackelberg game, and the downstream region provides economic compensation for green innovation investment in the upstream region. The results show that there is an optimal ecological compensation rate, and a Pareto improvement result can be obtained by implementing ecological compensation. Increasing the proportion of ecological compensation can improve the nonvirtuous chain reaction between green innovation investment cost, pollutant transfer rate, and ecological compensation rate. Therefore, it is necessary to establish a joint mechanism composed of the government and the market and formulate a reasonable green innovation subsidy scheme according to the actual situation of the basin, so as to restrict the emergence of this “individual rational” behavior. For river basin areas that can establish a unified management department and organize the implementation of decision-making, the cooperative game is a very effective pollution control decision.
Highlights
Since the late 1970s, the application of differential game theory has flourished in management science and economics
Differences from Jiang et al [33] are as follows: (i) it is not just the upstream region; in our model, both the upstream region and downstream region in a river basin can invest in pollution abatement. (ii) Different from the model of Jiang et al [33], in our model, the leader of the game is the downstream region who determines the ecological compensation rate firstly, the follower, e.g., the upstream region, decides the abatement investment under the given compensation rate. (iii) In our model, we consider the learning effect of two regions through green innovation investment to improve efficiency and reduce costs. e positive effects of learning by doing have been widely studied since Arrow [34]
E investment cost of green innovation is directly proportional to the ecological compensation rate
Summary
Since the late 1970s, the application of differential game theory has flourished in management science and economics. Ploeg et al [13] assumed that participants use a linear Markov perfect strategy and developed a differential game model to probe into the transboundary pollution issue, by which the cooperative and noncooperative Nash equilibrium results are reached. Differences from Jiang et al [33] are as follows: (i) it is not just the upstream region; in our model, both the upstream region and downstream region in a river basin can invest in pollution abatement (green innovation).
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