Application of Game Theory in Analyzing Urban and Rural Demographic Stability

Abstract

This paper examines the age-specific variations in marriage trends across urban and rural populations in India for males and females, utilizing data from the years 2005-2006, 2015-2016, and 2019-2021. Through a comparative analysis, the study explores the socio-economic and cultural factors influencing age at marriage, focusing on gender disparities and regional differences. Leveraging large-scale datasets, the research highlights trends in child marriage, delayed marriages, and shifts in societal norms over time. Furthermore, these variations are analyzed using game theory principles, applying the saddle point method to identify optimal strategies for addressing disparities in marriage age across rural and urban settings. By integrating mathematical frameworks with socio-demographic data, this paper provides a comprehensive understanding of how urbanization and policy interventions have impacted marriage age across genders and regions. The findings contribute to policy discourse, emphasizing the need for targeted interventions to address rural-urban disparities and ensure equitable development.This study analyzes demographic data of urban and rural populations for males and females across various age groups from 2005, 2015, and 2019 using game theory principles, specifically focusing on the concept of the saddle point. The saddle point represents an equilibrium in the data, where the row minimum equals the column maximum, indicating optimal stability in the dataset. Key observations reveal that urban male data for the age group 0–4 exhibits a saddle point of 9 in 2015, while rural male data demonstrates a saddle point of 10.2 in 2005 for the 5–9 age group. For females, urban areas show a saddle point of 9.1 in 2015, and rural areas exhibit a saddle point of 9.1 in 2019 for the 15–19 age group. The results highlight demographic shifts over time, including reductions the interplay of stability points in demographic data, emphasizing the role of equilibrium concepts in understanding temporal changes. The findings contribute to strategic planning in population percentages across various age groups. This game-theoretical analysis demonstrates in resource allocation and policy-making for urban and rural development.