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On the inducibility of Stackelberg Equilibrium for security games

On the inducibility of Stackelberg Equilibrium for security games
On the inducibility of Stackelberg Equilibrium for security games
Strong Stackelberg equilibrium (SSE) is the standard solution concept of Stackelberg security games. As opposed to the weak Stackelberg equilibrium (WSE), the SSE assumes that the follower breaks ties in favor of the leader and this is widely acknowledged and justified by the assertion that the defender can often induce the attacker to choose a preferred action by making an infinitesimal adjustment to her strategy. Unfortunately, in security games with resource assignment constraints, the assertion might not be valid; it is possible that the defender cannot induce the desired outcome. As a result, many results claimed in the literature may be overly optimistic.
To remedy, we first formally define the utility guarantee of a defender strategy and provide examples to show that the utility of SSE can be higher than its utility guarantee. Second, inspired by the analysis of leader’s payoff by Von Stengel and Zamir (2004), we provide the solution concept called the inducible Stackelberg equilibrium (ISE), which owns the highest utility guarantee and always exists. Third, we show the conditions when ISE coincides with SSE and the fact that in general case, SSE can be extremely worse with respect to utility guarantee. Moreover, introducing the ISE does not invalidate existing algorithmic results as the problem of computing an ISE polynomially reduces to that of computing an SSE. We also provide an algorithmic implementation for computing ISE, with which our experiments unveil the empirical advantage of the ISE over the SSE.
AAAI
Guo, Qingyu
9922ab2c-9e8f-484f-ae29-0455d5edc6b3
Gan, Jiarui
eaa9f4a0-ced7-48e9-b03e-ee10f21b76dc
Fang, Fei
0681e1db-6889-419c-94d4-77027f6979e7
Tran-Thanh, Long
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Tambe, Milind
a620fda8-c4fe-4193-a396-fe6de595fc6f
An, Bo
4b0743f9-91c9-4452-868c-1d12b4e9f456
Guo, Qingyu
9922ab2c-9e8f-484f-ae29-0455d5edc6b3
Gan, Jiarui
eaa9f4a0-ced7-48e9-b03e-ee10f21b76dc
Fang, Fei
0681e1db-6889-419c-94d4-77027f6979e7
Tran-Thanh, Long
e0666669-d34b-460e-950d-e8b139fab16c
Tambe, Milind
a620fda8-c4fe-4193-a396-fe6de595fc6f
An, Bo
4b0743f9-91c9-4452-868c-1d12b4e9f456

Guo, Qingyu, Gan, Jiarui, Fang, Fei, Tran-Thanh, Long, Tambe, Milind and An, Bo (2019) On the inducibility of Stackelberg Equilibrium for security games. In 33rd AAAI Conference on Artificial Intelligence. AAAI. 8 pp .

Record type: Conference or Workshop Item (Paper)

Abstract

Strong Stackelberg equilibrium (SSE) is the standard solution concept of Stackelberg security games. As opposed to the weak Stackelberg equilibrium (WSE), the SSE assumes that the follower breaks ties in favor of the leader and this is widely acknowledged and justified by the assertion that the defender can often induce the attacker to choose a preferred action by making an infinitesimal adjustment to her strategy. Unfortunately, in security games with resource assignment constraints, the assertion might not be valid; it is possible that the defender cannot induce the desired outcome. As a result, many results claimed in the literature may be overly optimistic.
To remedy, we first formally define the utility guarantee of a defender strategy and provide examples to show that the utility of SSE can be higher than its utility guarantee. Second, inspired by the analysis of leader’s payoff by Von Stengel and Zamir (2004), we provide the solution concept called the inducible Stackelberg equilibrium (ISE), which owns the highest utility guarantee and always exists. Third, we show the conditions when ISE coincides with SSE and the fact that in general case, SSE can be extremely worse with respect to utility guarantee. Moreover, introducing the ISE does not invalidate existing algorithmic results as the problem of computing an ISE polynomially reduces to that of computing an SSE. We also provide an algorithmic implementation for computing ISE, with which our experiments unveil the empirical advantage of the ISE over the SSE.

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Published date: 1 February 2019

Identifiers

Local EPrints ID: 431273
URI: https://eprints.soton.ac.uk/id/eprint/431273
PURE UUID: 21245c0d-ddd0-48f6-a04f-ad05be5a0b64
ORCID for Long Tran-Thanh: ORCID iD orcid.org/0000-0003-1617-8316

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Date deposited: 29 May 2019 16:30
Last modified: 30 Nov 2019 01:34

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Contributors

Author: Qingyu Guo
Author: Jiarui Gan
Author: Fei Fang
Author: Long Tran-Thanh ORCID iD
Author: Milind Tambe
Author: Bo An

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