This study examines the application of algorithmic game theory to politics, with a focus on developing optimal gerrymandering strategies. The paper begins by providing game theory and introducing key concepts of algorithmic game theory, focusing on its potential to analyze complex problems of political policy. Research then delves into political redistricting and gerrymandering, examining the historical development of these practices, examining the legal and ethical considerations involved, Addressing the computational challenges of gerrymandering problems, with NP rigor of some redistricting projects and the development of approximation algorithms to address these challenges are included. The review shows their applications in the context of redistricting, such as linear programming, integer linear programming, evolutionary algorithms, etc. It further explores optimization techniques for gerrymandering Integration of Geospatial Information Systems (GIS) The use of big data and machine learning in the redistricting process is also discussed. Through in-depth case studies, the paper examines historical examples and contemporary case studies of gerrymandering and illustrates the far-reaching effects of these practices on political representation, voter turnout, and racial bias so then the study addresses the concept of algorithmic fairness in redistricting, It examines fairness metrics and methods for reducing bias and unfairness Finally, the study explores the public policy implications of optimal gerrymandering strategies, considers legislative and judicial responses, and the role of redistricting commissions in reform proposals.