Information Design for Multiple Interdependent Defenders: Work Less, Pay Off More
Abstract
:1. Introduction
How can one obtain defense effectiveness and computation efficiency in multi-defender security games?
Comparison with Previous Works
2. Preliminary
3. Optimal Private Signaling
3.1. An Exponential-Size LP Formulation
3.2. A Polynomial-Time Algorithm
4. Optimal Ex Ante Private Signaling
4.1. An Exponential-Size LP Formulation
4.2. Compact Signaling Representation
- for all
- Every maximally covered target t, i.e., , is assigned to a defender; that is, .
- s.t
- s.t.
- …
- and such that where .
5. Experiments
6. Summary
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BCE | Bayes correlated equilibrium |
CPU | Central processing unit |
LHS | Left-hand side |
LP | Linear program |
MARL | Multi-agent reinforcement learning |
NSE | Nash Stackelberg equilibrium |
RHS | Right-hand side |
Appendix A. Proof of Lemma 4
Extension to Include Target Group
- s.t
- s.t.
- …
- and such that where .
Appendix B. Additional Experiments
1 | Notably, the defender can signal to the attacker as well, to either deter him from attacking or induce him to attack a specific target in order to catch him. Previous works have shown that this can benefit the defender [7,8] even though the attacker is fully aware of the strategic nature of the signal and will best respond to the revealed information. |
2 | This is without loss of generality, since any defender who can cover multiple targets can be “split” into multiple defenders with the same utilities. |
3 | The term “suggested” here should only be interpreted mathematically—i.e., given all the attacker’s available information, is identified as the most profitable target for the attacker to attack—and should not be interpreted as a real practice that the defender suggests the attacker to attack some target. Such a formulation, analogous to the revelation principle, is used for the convenience of formulating the optimization problem. |
4 | Such information can often by learned from informants such as local villagers [34]. |
5 | In reality, such a dummy target could be unimportant infrastructure (e.g., a nearby rest area at the border of a national park with no animals around, as in wildlife conservation), which does not matter to any defender nor the attacker. |
6 | Since we have targets in total while there are only defenders, some targets will not be assigned to any defenders. |
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Zhou, C.; Spivey, A.; Xu, H.; Nguyen, T.H. Information Design for Multiple Interdependent Defenders: Work Less, Pay Off More. Games 2023, 14, 12. https://doi.org/10.3390/g14010012
Zhou C, Spivey A, Xu H, Nguyen TH. Information Design for Multiple Interdependent Defenders: Work Less, Pay Off More. Games. 2023; 14(1):12. https://doi.org/10.3390/g14010012
Chicago/Turabian StyleZhou, Chenghan, Andrew Spivey, Haifeng Xu, and Thanh H. Nguyen. 2023. "Information Design for Multiple Interdependent Defenders: Work Less, Pay Off More" Games 14, no. 1: 12. https://doi.org/10.3390/g14010012