Çok hedefli savunma oyunlarında kaynak dağılımı

The optimal allocation of resources over the protection of several potential targets under a defense budget constraint is a challenging problem. In this thesis, we consider a game between an attacker and a defender who are competing over multiple targets. The defender has a limited amount of resources that need to be divided among multiple targets in an efficient manner. Our purpose is to identify the Nash equilibrium of this game, investigate the equilibrium investment strategy of the attacker and of the defender, gain insight into the allocation of the budget, and into the effects of changes in various model parameters, including the attacker's and the defender's valuations of the targets, the defense budget, and the efficiency of each party in their use of resources. While we consider also the sequential-move game where the defender decides first and the attacks follows, we mostly concentrate on the simultaneous-move game, where the parties decide simultaneously without observing each other's decisions. We solve the single-target problem explicitly, provide a characterization for the two-target problem, and propose a dynamic-programming formulation for the multi-target problem. We provide numerical examples to illustrate our model, results, and approach. Through these examples, we also make observations about the sensitivity of the equilibrium to changes in parameters, to the asymmetry of target valuations, and to the informational structure of the game.