Symmetric Case of Locks, Bombs and Testing Model

TL;DR

This paper introduces a game-theoretic model where a defender protects sites with locks and an attacker destroys them with bombs, incorporating imperfect testing to determine optimal resource allocation strategies.

Contribution

It presents the first analysis of a Locks-Bombs-Testing model with imperfect testing, focusing on identical sites and fixed lock numbers for the defender.

Findings

Derived optimal strategies for the special case of identical sites.

Analyzed the impact of imperfect testing on resource allocation.

Provided insights into strategic decision-making under uncertainty.

Abstract

We present a Defense/Attack resource allocation model, where Defender has some number of ``locks" to protect $n$ vulnerable boxes (sites), and Attacker is trying to destroy these boxes, having $m$ ``bombs" that can be placed into the boxes. Similar models were studied in game theory - (Colonel) Blotto games, but our model has a feature absent in the previous literature. Attacker tests the vulnerability of all sites before allocating her resources, and these tests are not perfect, i.e., a test can be positive for a box without a lock and negative for a box with a lock. We describe the optimal strategies for a special case of a general Locks-Bombs-Testing (LBT) model when all boxes are identical and the Defender has a fixed number of locks.