With the background of aging, ensuring the deep integration of pension and medical services and effectively integrating pension resources and medical resources are hot issues that must be addressed in the current mode of integrating health and care services for older people. Thus, we use game theory to construct the utility model of resource allocation between pension and medical institutions. We apply this model to explore how pension institutions and medical institutions invest resources into the integration of health and care services, analysis of influencing factors, and conducting incentive mechanism research by using MATLAB 2016b software. Through theoretical deduction and experimental analysis, the following conclusions are drawn. First, the income distribution coefficient of pension institutions is positively correlated with the level of labor input, and its growth rate has a marginal diminishing effect on the level of labor. Second, in early investment, the income distribution coefficient of pension institutions is positively correlated with fixed asset investment regardless of the different effort coefficients between medical institutions and pension institutions. With a high income distribution coefficient, pension institutions are negatively correlated and marginally decrease. Third, in early investment, the income distribution coefficient of pension institutions is positively correlated with medical institutions’ labor input level. When the income distribution coefficient of pension institutions reaches a certain value, it is negatively correlated with the labor input level of medical institutions, thereby showing a marginal diminishing effect.

中文翻译：

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老年人保健服务一体化的演化博弈模型

在老龄化的背景下，确保养老金和医疗服务的深度融合以及有效地整合养老金和医疗资源是当前为老年人提供医疗和护理服务的一体化模式中必须解决的热点问题。因此，我们用博弈论来构建养老金和医疗机构之间资源分配的效用模型。我们使用此模型来探索养老金机构和医疗机构如何将资源投入到医疗保健服务的整合，影响因素的分析以及使用MATLAB 2016b软件进行激励机制研究中。通过理论推导和实验分析，得出以下结论。第一，养老金机构的收入分配系数与劳动投入水平呈正相关，其增长率对劳动水平具有边际递减作用。其次，在早期投资中，养老金机构的收入分配系数与固定资产投资呈正相关，而与医疗机构和养老金机构之间的劳动系数不同。收入分配系数高时，养老金机构负相关并略有减少。第三，在早期投资中，养老机构的收入分配系数与医疗机构的劳动投入水平呈正相关。当养老金机构的收入分配系数达到一定值时，