Bankruptcy situtations and modeling with game theory

Game theory is a sub-discipline of mathematics that examines the social consequences of decisions made by rational individuals and bases these investigations on mathematical foundations. This discipline analyzes various situations in which individuals interact with each other, and examines in detail their strategic choices and their impact on society. Game theory is a comprehensive method of analysis that can be applied in many economic, social and political fields. Cooperative game theory is one of the sub-branches of game theory that aims to analyze the decision-making mechanisms through which players come together to form coalitions in which the payoffs are shared. This theory provides a comprehensive framework for determining optimal strategies, taking into account the individual interests of the players and their interactions within the coalition. Thus, cooperative game theory helps to identify optimal strategies in different scenarios by mathematically analyzing the processes of cooperation and joint decision-making. Bankruptcy problems are a field that investigates how to allocate a given resource among various groups of players in the fairest way according to the demands of the players and aims to solve these complex situations using game theory and mathematical models. This field examines the solutions developed to ensure that the allocation of resources is fair and efficient. Solutions to insolvency problems help to ensure that the sharing process is conducted in a fair manner, taking into account the demands of each player, and that this process is handled within a framework based on mathematical foundations. This thesis is a study on bankruptcy situations and bankruptcy games modeled by game theory. First, a comprehensive overview of the basic concepts of cooperative game theory is presented. Then, the bankruptcy games and solution methods obtained as a result of bankruptcy cases are given. Finally, by using the RUN rule, PROP rule, Shapley value, Banzhaf value, CIS value and ENSC value, which are commonly used solutions in bankruptcy cases, a model is worked on that aims to make the fairest allocation considering the demands of the companies and the resources of the bank as a result of the fact that the loan amounts demanded by three different companies from a bank cannot be fully covered by the bank