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In competitive scenarios, we analyze the optimal pricing, launch timing, and influencing factors of new products by establishing three differential game models. The findings indicate that (1) the depreciation rate of old products directly impacts the pricing strategies of advantaged and disadvantaged enterprises. Enterprises with competitive advantages tend to set higher prices for new products when old products depreciate faster, while those with fewer advantages adjust their pricing strategies by initially increasing prices for the latest prices and eventually reducing them. (2) The rate of old‐product depreciation also affects the timing of new‐product launches. Advantaged enterprises tend to delay their product launches when the impact of the new product on the old ones is significant, while disadvantaged enterprises opt for earlier launches under similar circumstances. (3) The technological level of the new product influences the timing of its launch for both advantaged and disadvantaged enterprises. Higher technological levels prompt advantaged enterprises to launch earlier and disadvantaged enterprises tend to follow suit. (4) High levels of innovation in new products by advantaged enterprises prompt earlier launches by disadvantaged enterprises. These results may offer valuable insights for enterprises in formulating effective product rollover strategies. [ABSTRACT FROM AUTHOR]

This study explores whether the government should implement a cost-sharing or penalty mechanism to control waste incineration pollution and investigates which policy can best incentivize incineration plants to invest in pollution control. We design two differential game models, one based on a cost-sharing approach and one on a penalty system, to model the interactions between the government and incineration plants. We then compare and analyze the equilibrium outcomes in both scenarios. Our findings reveal that when incineration pollution significantly impacts the government, both the cost-sharing and penalty mechanisms are effective in stimulating incineration plants to enhance their pollution control efforts. However, when incineration pollution significantly affects the incineration plants themselves, the cost-sharing mechanism proves to be more effective in terms of pollution control. Furthermore, we find that the government derives greater utility under the cost-sharing mechanism compared with the penalty mechanism, especially as the amount of municipal solid waste (MSW) increases. In contrast, incineration plants tend to generate higher profits under the cost-sharing mechanism. These findings and their accompanying managerial implications may provide valuable guidance for government agencies in formulating policies to manage incineration pollution and encourage waste incineration plants to invest in improving their pollution control systems. Funding: This work was supported by the National Natural Science Foundation of China [Grant 71571149], Humanities and Social Sciences Foundation for Youth Scholars of Ministry of Education of China [Grant 22YJC630171], and Natural Science Foundation of Sichuan Province of China [Grant 2023NSFSC1055]. [ABSTRACT FROM AUTHOR]

The differential game method effectively reflects the multi-agent, long-term, and dynamic characteristics of combating regional desertification. Considering the differences in the levels of economic development level and governance technology between adjacent areas, three desertification-combating modes are proposed for exploratory purposes. The differential game models of the two regions combating desertification areas are constructed as per the certain level of cooperation, ecological subsidy, and technology transfer modes. The optimal combating mode is found by comparing the equilibrium results. The study demonstrates that when cooperation level dominated by the region with higher economic and governance technology levels is lower than the threshold $ \phi^{*}_{u_2} $ and $ \phi^{*}_{1V} $, the technology transfer mode is optimal, and the level of cooperation does not affect the technology transfer fee. However, when cooperation level is higher than the threshold $ \phi^{*}_{u_2} $ and $ \phi^{*}_{1V} $, the ecological subsidy mode is optimal. Meanwhile, as the dominant region further raises the cooperation level, it can drive the non-dominant region to increase the desertification combating input level. The certain level of cooperation mode is the least efficient of the three modes. However, when compared with the situation of completely independent governance by the two regions, the certain level of cooperation mode can relatively improve the efficiency of regional desertification combating. [ABSTRACT FROM AUTHOR]

The problem of desertification is becoming increasingly severe, affecting the production and livelihood of people; this has led to keen interest in the issue, especially in developing countries. Based on the dynamic changes in desertification control scale and enterprise goodwill, we studied the game problem of desertification control between the government and enterprise under the non-cooperative, cost-sharing, and cooperative modes by constructing a differential game model. We put forward a revenue distribution mechanism with time consistency under the cooperation mode. The results show that government and enterprise control of desertification under the cooperative mode has the best effect, followed by the cost-sharing mode. The non-cooperative mode should be avoided. Lowering tax rates by the government is not always a good method of encouraging enterprises to increase desertification control investment. The tax rate should be adjusted according to the choice of governance mode as it can more effectively increase the investment level of enterprises in combating desertification. The optimal pricing of desert characteristic products is not affected by the governance mode. [ABSTRACT FROM AUTHOR]