On the Characterization of Saddle Point Equilibrium for Security Games with Additive Utility

TL;DR

This paper analyzes a class of security games with additive utility functions, revealing structural properties and proposing a linear-time algorithm for computing game value, significantly improving computational efficiency for large-scale instances.

Contribution

It introduces a structural analysis of additive utility security games and develops a linear-time algorithm for computing the game value, enhancing scalability.

Findings

Structural properties of optimal strategies identified.

Linear-time algorithm for value computation proposed.

Improved computational efficiency over previous methods.

Abstract

In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore, computing the value and optimal strategy for the players becomes computationally expensive. In this work, we analyze a special class of zero-sum games in which the payoff matrix has a special structure which results from the {\it additive property} of the utility function. Based on variational principles, we present structural properties of optimal attacker as well as defender's strategy. We propose a linear-time algorithm to compute the value based on the structural properties, which is an improvement from our previous result in \cite{emadi2019security}, especially in the context of large-scale zero-sum games.