Investigation of facility allocation games on graphs using game theory

This thesis explores the Voronoi game, a strategic competition model that combines principles from game theory and computational geometry. In the Voronoi game, players are placed within a bounded space, and territory is determined by proximity, forming regions called Voronoi cells. The objective is to capture the maximum area within these cells, leading to complex strategic behaviors. This study investigates the core mechanics, variations, and applications of the Voronoi game, as well as its implications for broader fields such as network design, facility location, and competitive spatial strategies. Through analytical and computational approaches, we characterize equilibria, evaluate player strategies, and explore multi-round dynamics, providing a comprehensive understanding of the games mathematical and practical relevance.