Exploring Information Asymmetry in Two-Stage Security Games

Transcription

1 Exploring Information Asymmetry in Two-Stage Security Games Haifeng Xu 1, Zinovi Rabinovich 2, Shaddin Dughmi 1, Milind Tambe 1 1 University of Southern California 2 Independent Researcher

2 Security Games Background Stackelberg Games Defender/Attacker players Protect a set of targets using limited resources Flights Roads Ports Wildlife Strong Stackelberg Equilibrium 2 /54

3 What is Defense? (Randomly) allocate resources to protect targets Shape the attacker s belief on the protection of targets. E.g., manipulate the information regarding the game to bias the attacker s belief Protected? Probably! 3 /54

4 Information & Beliefs Attacker s belief depends on the information he has Information asymmetry gives rise to manipulation Widely studied in economics [2001 Nobel Prize] In security: defender usually has more information How should defender make use of additional information for strategic gain? 4 /54

5 Contributions Initiate the study of strategic information in security Show when (always?) and how (optimally?) can information help? 5 /54

6 Outline An Example Domain Information Revelation Scheme General Modeling and Results 6 /54

7 Outline An Example Domain Information Revelation Scheme General Modeling and Results 7 /54

8 Example Domain: Fare Evasion Fare Evasion in LA Metro System [Yin et al. 2012] Proof-of-payment Estimated annual loss: $5.6 million 300,000 rider daily ( 2.5% evader) 8 /54

9 Example Domain: Fare Evasion Traditionally: /54

10 Example Domain: Fare Evasion Traditionally: p:0.2 1 Another option is to buy a ticket; both get 0. 1 p:0.2 2 defu = evau = 0.4 p: /54

11 Zoom in: Example Domain: Fare Evasion Protected? Yes! Protected? p=0.2 Station announces a message -- an inspector is inside! Unfortunately, such lucky chance happens with p=0.2 Is there a smarter way? 11 /54

12 Outline An Example Domain Information Revelation Scheme General Modeling and Results 12 /54

13 A Strategic Way Twomessages m c or m 0.2 u : covered 0.2 Persuasion m c P(cover m evau 0; 0.8 c ) 1/ 4; P(uncover m defu 1 Buy defu =0 c ) 3/ uncovered m u evau = 2 defu = -2 In expectation, defu = -0.4 ( > -1.2 ); evau = 0.4 (no change) 13 /54

14 Persuasion in a Nutshell 0.2 P(cover m evau 0; c ) 1/ 4; P(uncover defu 1 m c ) 3/ covered m c uncovered m u A posterior, which is bad for both players Persuasion Scheme identifies such a posterior, and signal it to the evader 14 /54

15 Outline An Example Domain Information Revelation Scheme General Modeling and Results 15 /54

16 Modeling A natural two-stage security game model Phase 1: scheduling (as regular security games) Phase 2 : strategically reveal information at each target (persuasion) 16 /54

17 Assumption Questions Why should the attacker follow the persuasion scheme? His best response, given the information Why should the defender honestly send signals? Signaling scheme should be trustful Why breaks tie in favor of the defender? Without loss of generality 17 /54

18 Theoretical Results When would the defender strictly benefit by information (notice that the defender is never worse off)? provide a succinct iff characterization No benefit in zero-sum games How would the attacker s utility change? Does not change if the defender persuade optimally How to do both phases optimally? Phase 2: an LP for each target, parameterized by marginal coverage Phase 1 the Strong Stackelberg Equilibrium (SSE) of its standard version -- need to consider the effect of phase 2 Algorithm: multiple LPs and the same complexity as computing SSE 18 /54

19 Theoretical Results When would the defender strictly benefit by information (notice that the defender is never worse off)? The paper provides a succinct iff characterization No benefit in zero-sum games How would the attacker s utility change? Does not change if the defender persuade optimally How to do both phases optimally? Phase 2: an LP for each target, parameterized by marginal coverage Phase 1 the Strong Stackelberg Equilibrium (SSE) of its standard version -- need to consider the effect of phase 2 Algorithm: multiple LPs and the same complexity as computing SSE 19 /54

20 Theoretical Results When would the defender strictly benefit by information? (notice that the defender is never worse off) The paper provides a succinct iff characterization No benefit in zero-sum games How would the attacker s utility change? Does not change if the defender persuade optimally How to do both phases optimally? Phase 2: an LP for each target, parameterized by marginal coverage Phase 1 the Strong Stackelberg Equilibrium (SSE) of its standard version -- need to consider the effect of phase 2 Algorithm: multiple LPs and the same complexity as computing SSE 20 /54

21 Simulations Measures proximity to zero-sum 21 /54

22 Open Problems General extensive form games? Other type of information? Defender s knowledge about resources, targets, environments. Human behavior models (irrational attacker) Information asymmetry in general strategic interactions 22 /54

23 Thanks Q&A 23 /54