An application on mountain situations by using cooperative game theory

Cooperative game theory is a theoretical framework that explores how economic benefits and costs can be distributed fairly and efficiently among individuals. This theory holds a significant place in various fields, particularly in operations research and economic modeling. In general, a game refers to situations in which multiple players make strategic decisions in mutual interaction. Game theory focuses on analyzing structures where the strategic choices of players are directly influenced by the actions of others, examining how each player can determine the most rational strategy under specific conditions. In scenarios where a player's outcome depends on the decisions of others, identifying the optimal course of action becomes the central concern.Throughout history, individuals, institutions, businesses, states, and leaders have engaged in ongoing competition to protect and strengthen their interests. The strategies developed within this competitive environment have not only impacted the actors themselves but also influenced other stakeholders and the overall functioning of the system.The foundations of game theory were laid through the contributions of pioneering scholars such as John von Neumann, Oskar Morgenstern, and John Nash. Since the 1980s, it has been widely adopted as an effective analytical tool, particularly in fields like economics and political science, and has taken on an interdisciplinary character. This study examines mountain situations (tree structures) modeled within the framework of cooperative game theory and associated with minimum-cost tree formations. Initially, the fundamental concepts of cooperative game theory are introduced. Then, the cooperative games that emerge from modeling mountain situations through game theory and the corresponding solution approaches are analyzed in detail. Finally, the study presents an applied example based on a flood disaster that occurred in Türkiye, illustrating the practical implementation of the theoretical model.