We consider a security game in a setting consisting of two players (an attacker and a defender), each with a given budget to allocate towards attack and defense, respectively, of a set of nodes. Each node has a certain value to the attacker and the defender, along with a probability of being successfully compromised, which is a function of the investments in that node by both players. For such games, we characterize the optimal investment strategies by the players at the (unique) Nash Equilibrium. We then investigate the impacts of behavioral probability weighting on the investment strategies; such probability weighting, where humans overweight low probabilities and underweight high probabilities, has been identified by behavioral economists to be a common feature of human decision-making. We show via numerical experiments that behavioral decision-making by the defender causes the Nash Equilibrium investments in each node to change (where the defender overinvests in the high-value nodes and underinvests in the low-value nodes).
翻译:在由两个参与者(攻击者和捍卫者)组成的环境下,我们考虑一个安全游戏,每个参与者都有各自的预算用于攻击和防御一组节点。每个节点对攻击者和捍卫者都有一定的价值,还有成功妥协的可能性,这是两个参与者在节点上投资的函数。对于这种游戏,我们描述(独角兽)Nash 平衡的参与者的最佳投资策略。 然后我们调查行为概率对投资战略的影响;当行为经济学家发现人超重低概率和体重不足高概率时,概率加权是人类决策的共同特征。 我们通过数字实验显示,捍卫者的行为决策导致对每个节点的纳什平衡投资(在高价值节点上投资,低价值节点投资不足 ) 。