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Games
Volume 15
Issue 5
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Games, Volume 15, Issue 5 (October 2024) – 5 articles

Cover Story (view full-size image): The article "Vulnerability and Defence: A Case for Stackelberg Game Dynamics" explores strategic interactions between opposing entities in military operations through game theory. By applying the principles of Stackelberg equilibrium and backward induction, it models these interactions as a sequential game, with one side leading and the other responding. This paper provides insights into optimizing both offensive and defensive strategies, demonstrating how modern conflicts reflect dynamic decision-making. It also emphasizes the importance of understanding the interplay between rational actors in military settings, presenting a compelling case for applying game theory to real-world defence scenarios. View this paper
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25 pages, 22933 KiB  
Article
Simulation of the Stackelberg–Hotelling Game
by Luis Garcia-Perez, Juan Grau-Climent, Juan C. Losada and Ramon Alonso-Sanz
Games 2024, 15(5), 34; https://doi.org/10.3390/g15050034 - 11 Oct 2024
Viewed by 735
Abstract
This work studies the Hotelling game with sequential choice of prices, that is, the Stackelberg–Hotelling (SHOT) game. The game is studied through numerical simulation, which provides the subgame perfect equilibrium solution not only in the unrestricted game but also in the game with [...] Read more.
This work studies the Hotelling game with sequential choice of prices, that is, the Stackelberg–Hotelling (SHOT) game. The game is studied through numerical simulation, which provides the subgame perfect equilibrium solution not only in the unrestricted game but also in the game with reservation cost and with elastic demand. The simulation technique is tested first in the unconstrained game, where the analytical subgame perfect equilibrium solution was already known. Then, the numerical procedure is generalized to cope with the SHOT game with reservation cost and with elastic demand. These enriched formulations of the SHOT game have not been studied so far, so this article provides an exploratory study of them. Full article
(This article belongs to the Section Algorithmic and Computational Game Theory)
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16 pages, 2265 KiB  
Article
A Solution to Dynamic Weapon Assignment Problem Based on Game Theory for Naval Platforms
by Oğuzkan Akbel and Aykut Kalaycıoğlu
Games 2024, 15(5), 33; https://doi.org/10.3390/g15050033 - 6 Oct 2024
Viewed by 718
Abstract
Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem’s complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) [...] Read more.
Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem’s complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) and dynamic (considering changes over time). Static systems solve the problem for a single time step without considering temporal changes. Dynamic systems incorporate time as a variable, adapting to evolving scenarios. Two main approaches exist, which are asset-based and target-based. Asset-based approach maximizes the survival probability of assets, which is our focus in this study. We propose a solution using game theory that spans the entire area and all time frames. We employ game theory, treating continuous functions of time as utility functions for vessels. Continuous probability-to-kill values for weapons are defined across the area. Threat trajectories yield continuous kill probabilities for the weapons, translating to vessel utility. To avoid inefficiencies, we align individual vessel utility with global utility. The Nash Equilibrium provides the optimal weapon assignment strategy. Our study uses a naval environment for analysis. In summary, our research leverages game theory to dynamically assign weapons to naval vessels, aiming to maximize asset survival. Full article
(This article belongs to the Section Applied Game Theory)
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13 pages, 1201 KiB  
Article
Vulnerability and Defence: A Case for Stackelberg Game Dynamics
by Azhar Iqbal, Ishan Honhaga, Eyoel Teffera, Anthony Perry, Robin Baker, Glen Pearce and Claudia Szabo
Games 2024, 15(5), 32; https://doi.org/10.3390/g15050032 - 18 Sep 2024
Viewed by 860
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 [...] Read more.
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. Full article
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17 pages, 352 KiB  
Article
Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation
by Eunmi Ko
Games 2024, 15(5), 31; https://doi.org/10.3390/g15050031 - 11 Sep 2024
Viewed by 551
Abstract
I consider a class of dynamic Bayesian games in which types evolve stochastically according to a first-order Markov process on a continuous type space. Types are privately informed, but they become public together with actions when payoffs are obtained, resulting in a delayed [...] Read more.
I consider a class of dynamic Bayesian games in which types evolve stochastically according to a first-order Markov process on a continuous type space. Types are privately informed, but they become public together with actions when payoffs are obtained, resulting in a delayed information revelation. In this environment, I show that there exists a stationary Bayesian–Markov equilibrium in which a player’s strategy maps a tuple of the previous type and action profiles and the player’s current type to a mixed action. The existence can be extended to K-periodic revelation. I also offer a computational algorithm to find an equilibrium. Full article
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22 pages, 722 KiB  
Article
Nash Equilibria and Undecidability in Generic Physical Interactions—A Free Energy Perspective
by Chris Fields and James F. Glazebrook
Games 2024, 15(5), 30; https://doi.org/10.3390/g15050030 - 26 Aug 2024
Viewed by 1217
Abstract
We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in [...] Read more.
We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view. Full article
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