Citation: Iqbal, A.; Honhaga, I.; Teffera, E.; Perry, A.; Baker, R.; Pearce, G.; Szabo, C. Vulnerability and Defence: A Case for Stackelberg Game Dynamics. Games 2024, 15, 32. https://doi.org/ 10.3390/g15050032 Academic Editor: Ulrich Berger Received: 27 July 2024 Revised: 13 September 2024 Accepted: 14 September 2024 Published: 18 September 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). games Article Vulnerability and Defence: A Case for Stackelberg Game Dynamics Azhar Iqbal 1, * , Ishan Honhaga 1 , Eyoel Teffera 2 , Anthony Perry 2 , Robin Baker 2 , Glen Pearce 2 and Claudia Szabo 1 1 School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia; ishan.honhaga@adelaide.edu.au (I.H.); claudia.szabo@adelaide.edu.au (C.S.) 2 Defence Science and Technology Group, P.O. Box 1500, Edinburgh, SA 5111, Australia; eyoel.teffera@defence.gov.au (E.T.); ant.perry@defence.gov.au (A.P.); robin.baker@defence.gov.au (R.B.); glen.pearce@defence.gov.au (G.P.) * Correspondence: azhar.iqbal@adelaide.edu.au Abstract: This paper examines the tactical interaction between drones and tanks in modern warfare through game theory, particularly focusing on Stackelberg equilibrium and backward induction. It describes a high-stakes conflict between two teams: one using advanced drones for attack, and the other defending using tanks. The paper conceptualizes this as a sequential game, illustrating the complex strategic dynamics similar to Stackelberg competition, where moves and countermoves are carefully analyzed and predicted. Keywords: Stackelberg equilibrium; sequential games; backwards-induction outcome 1. Introduction More than a century before John Nash formalized the concept of equilibrium in game theory [1–3], Antoine Cournot [4] had already introduced a similar idea through his duopoly model, which became a cornerstone in the study of industrial organization [5]. In economics, an oligopoly refers to a market structure in which a small number of firms (n ≥ 2) supply a particular product. A duopoly, a specific case where n = 2, is the scenario to which Cournot’s model applies. In this model, two firms simultaneously produce and sell a homogeneous product. Cournot identified an equilibrium quantity for each firm, where the optimal strategy for each participant is to follow a specific rule if the other firm adheres to it. This idea of equilibrium in a duopoly anticipated Nash’s more general concept of equilibrium points in non-cooperative games. In 1934, Heinrich von Stackelberg [6,7] introduced a dynamic extension to Cournot’s model by allowing for sequential moves rather than simultaneous ones. In the Stackelberg model, one firm, the leader, moves first, while the second, the follower, reacts accordingly. A well-known example of such strategic behavior is General Motors’ leadership in the early U.S. automobile industry, with Ford and Chrysler often acting as followers. The Stackelberg equilibrium, derived through backward induction, represents the optimal outcome in these sequential-move games. This equilibrium is often considered more robust than Nash equilibrium (NE) in such settings, as sequential games can feature multiple NEs, but only one corresponds to the backward-induction outcome [1–3]. 2. Related Work Stackelberg games have been significantly influential in security and military research applications [8–19]. These games, based on the Stackelberg competition model, have been successfully applied in a wide range of real-world scenarios. They are particularly notable for their deployment in contexts where security decisions are critical, such as in protecting infrastructure and managing military operations. The sequential setup of Stackelberg games is particularly relevant in military contexts where strategic decisions often involve anticipating and responding to an adversary’s Games 2024, 15, 32. https://doi.org/10.3390/g15050032 https://www.mdpi.com/journal/games