Symmetric Case of Locks, Bombs and Testing Model
Computer Science and Game Theory
2023-07-06 v1 Optimization and Control
Probability
Abstract
We present a Defense/Attack resource allocation model, where Defender has some number of ``locks" to protect vulnerable boxes (sites), and Attacker is trying to destroy these boxes, having ``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.
Cite
@article{arxiv.2307.01810,
title = {Symmetric Case of Locks, Bombs and Testing Model},
author = {Isaac M. Sonin},
journal= {arXiv preprint arXiv:2307.01810},
year = {2023}
}