Should I Regret More? A Regret-based Multi-round Learning with Behavioral Human Players in a Multi-Target Security Game

We consider a security game in a setting consisting of an attacker and multiple defenders. Both defenders and attacker have limited budgets such that they can select subsets of the nodes to defend and attack, respectively. Each node has a certain gain and loss to the attacker and the defender, respectively. Each node has also a probability of being successfully compromised, which is a function of the investments in that node by the defenders. For such games, we investigate the impacts of behavioral probability weighting on the strategies of the players; 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 explore the multi-round game under regret-matching and prove the convergence to correlated equilibrium in our game. We then show the effect of the behavioral bias on the convergence of the regret-matching learning. Finally, we show via numerical experiments that the regret-matching algorithm is effective for both behavioral and rational defenders (i.e., it helps both classes of defenders to converge to better investments over time)