The Effect of Behavioral Probability Weighting in a Simultaneous Multi-Target Attacker-Defender Game

TL;DR

This paper analyzes a security game with two players, exploring how behavioral probability weighting influences optimal investment strategies and equilibrium outcomes in attack-defense scenarios.

Contribution

It introduces the impact of human-like probability weighting on Nash Equilibrium strategies in multi-target security games.

Findings

Behavioral probability weighting alters investment strategies.

Defender overinvests in high-value nodes.

Underinvestment occurs in low-value nodes.

Abstract

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).