# The impact of wage structure and ability on the incentives for practitioners to engage in primary care in China: a mathematical analysis based on the incentive mechanism of heterogeneous practitioners and tripartite evolutionary game

## TL;DR

This paper uses mathematical models to explore how wage structures and practitioner ability influence participation in primary healthcare in China.

## Contribution

The paper introduces a tripartite evolutionary game model to analyze general practitioner incentives and wage structure reforms in primary healthcare.

## Key findings

- High-quality practitioners receive information rent under separating equilibrium, while less experienced ones face allocation distortion.
- Reducing performance risk for less experienced practitioners increases their performance wage when their risk is equal to or higher than high-quality practitioners.
- Adjusting wage structures by increasing the floating part encourages participation and skill improvement among practitioners.

## Abstract

This study aims to analyze how wage structure and individual ability affect practitioners' participation in primary healthcare.

This study employs a mixed moral hazard and adverse selection model to analyze the optimal performance-based wage for general practitioners under separating and pooling equilibrium. Subsequently, we utilize tripartite evolutionary games to analyze the dynamic process of participation strategies to the primary health care with high—and less experienced practitioners.

Our study yields four main findings: (1) Under an effective separating equilibrium, high-quality practitioners receive information rent, and there is no distortion at the top, while less experienced practitioners face allocation distortion. (2) When the performance risk of less experienced practitioners is greater than or equal to that of high-quality practitioners, reducing the performance risk of less experienced practitioners is an effective method of increasing their performance wage. Conversely, when the performance risk of less experienced practitioners is less than that of high-quality practitioners, and they can transform into high-quality practitioners by increasing education costs, they will be incentivized to continue as general practitioners, provided there is a precise promotion mechanism. (3) If reforms are made to the wage structure in primary healthcare, an effective approach is to increase the proportion of the floating part. This would lead primary healthcare institutions to choose contracts under separating equilibrium, encouraging high-quality practitioners to participate in primary healthcare and less experienced practitioners to improve their abilities by increasing education costs. However, the proportion of the floating part in the wage structure should not be excessively large. (4) The effective cost of medical resource utilization influences the wage structure, and establishing reasonable upper and lower limits for performance wages can effectively increase the incentive for high-quality practitioners to participate in primary healthcare.

For the first time, our study employs a tripartite evolutionary game model to analyze the development of the general practitioner system. We analyze how the reform of the wage structure can encourage more practitioners to participate in primary healthcare. Our findings can lay the theoretical foundation for subsequent empirical analyses. Moreover, our findings provide theoretical assistance for government decisions and healthcare institutions.