Table 1.
Variations introduced in the stochastic duel game model over time.
| S. No. | Year | Resource | Novelty(s) | Intended Application Domain | Type of Proposed Model | |||
|---|---|---|---|---|---|---|---|---|
| One-on-One | Two-on-One | Many-on-One | Many-on-Many | |||||
| 1 | 1963 | Stochastic Duels [2] | Theory of stochastic duels introduced. | Military | ✔ | ✗ | ✗ | ✗ |
| 2 | 1966 | The status of developments in the theory of stochastic duels—2 by Ancker Jr, C. J. [3] | The fundamental duel introduced, and developments in basic duel theory with respect to military combats discussed. | Military | ✔ | ✗ | ✗ | ✗ |
| 3 | 2011 | A kind of stochastic duel model for guerrilla war—Liwei Liu, Jun Yua, ZhiGuob [7] | Concept of war as a duel between teams (forces) introduced. Combat between terrorists and organized forces discussed. | Military | ✗ | ✔ | ✗ | ✔ |
| 4 | 2020 | Antagonistic One-To-N Stochastic Duel Game by Song-Kyoo (Amang) Kim [16] | “One player shooting to kill all others” concept introduced, and application in Red/Blue Ocean markets discussed. | Civil | ✗ | ✗ | ✔ | ✗ |
| 5 | 2020 | A Versatile Stochastic Duel Game by Song-Kyoo (Amang) Kim [17] | Time-based stochastic game model introduced, and application in business strategies discussed. | Civil | ✔ | ✗ | ✗ | ✗ |
| 6 | 2021 | Robust Pairwise n-Person Stochastic Duel Game by Song-Kyoo (Amang) Kim [18] | Concept of n-players in multiple battlefields introduced following a pair-wise duel. | Civil | ✔ | ✗ | ✗ | ✗ |
| 7 | 1979 | The One-on-One Stochastic Duel: Parts I and II—Anker Jr, C.J. [19] | A summary of all the formulations conducted to date is given to help future research. | Military | NA | NA | NA | NA |
| 8 | 1980 | Stochastic Duels with Multiple Hits, and Fixed Duel Time—Kwon, T.; Bai, D. [20] | Constraints on the original stochastic duel model applied. Results are discussed for duel with fixed time and are extended to multiple hit–kill possibilities. | Military | ✔ | ✗ | ✗ | ✗ |
| 9 | 1983 | Stochastic duels with multiple hits and limited ammunition supply—Kwon, T.; Bai, D. [21] | Constraints on the original stochastic duel model discussed. Results discussed for duel with limited ammunition supply, and possibility of multiple hits considered. | Military | ✔ | ✗ | ✗ | ✗ |
| 10 | 1983 | Some stochastic duel models of combat by Jum Soo Choe [22] | Results for multiple-duel model discussed for discrete and continuous firing times. | Military | ✔ | ✗ | ✗ | ✗ |
| 11 | 1984 | The two-on-one stochastic duel—Gafarian, A.; Ancker, C.J. [23] | A new model of two-on-one type is introduced, and results for the same are derived. | Military | ✗ | ✔ | ✗ | ✗ |
| 12 | 1987 | The many-on-one stochastic duel by Kress, M. [24] | State probabilities for the many-on-one model are derived, and results are illustrated using an example. | Military | ✗ | ✗ | ✔ | ✗ |
| 13 | 1992 | A many-on-many stochastic duel model for a mountain battle—Kress, M. [25] | Practical application of the theory of stochastic duels in a mountain battle scenario and its results are discussed. | Military | ✗ | ✗ | ✗ | ✔ |
| 14 | 1993 | Explicit modeling of detection within a stochastic duel—K. Wand, S. Humble, R. J. T. Wilson [26] | Concept of target detection in a duel introduced. Duel between two weapon systems discussed. | Military | ✗ | ✔ | ✗ | ✗ |
| 15 | 1997 | An Introduction to Applicable Game Theory—Gibbons, R. [27] | An economic use case of gametheory is explored, and usability is justified with an example. | Civil | NA | NA | NA | NA |
| 16 | 2012 | The Many-on-One Stochastic Duel Model with Information-Sharing—Li, J.; Liu, L. [28] | A many-on-one extension is drawn from the original one-on-one stochastic duel model, and results are derived on the basis of information sharing. | Military | ✗ | ✗ | ✔ | ✗ |
| 17 | 2013 | New results on a stochastic duel game with each force consisting of heterogeneous units by Kyle Y. Lin [29] | A two-person zero-sum game is discussed as part of combat between two forces, and an algorithm to compute the strategy is given. | Military | ✗ | ✗ | ✗ | ✔ |
| 18 | 2017 | Aircraft Evaluation Using Stochastic Duels—Gay, Jason W. [30] | Evaluation of performance of fighter aircraft in air combat conducted, and one-on-one aerial combat discussed. | Military | ✔ | ✗ | ✗ | ✗ |
| 19 | 2022 | Game Theory in Defence Applications: A Review—Ho, E.; Rajagopalan, A.; Skvortsov, A.; Arulampalam, S.; Piraveenan, M. [31] | Literature review of many attempts to use game theory in decision-making scenarios for military-based application is conducted. Details about specific models are also discussed. | Military | NA | NA | NA | NA |
✔: Yes, ✗: No, NA: Not Applicable.