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CPS 173 Security games

CPS 173 Security games. Vincent Conitzer conitzer@cs.duke.edu. Recent deployments in security. Tambe’s TEAMCORE group at USC Airport security Where should checkpoints, canine units, etc. be deployed? Deployed at LAX and another US airport, being evaluated for deployment at all US airports

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CPS 173 Security games

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  1. CPS 173Security games Vincent Conitzer conitzer@cs.duke.edu

  2. Recent deployments in security • Tambe’s TEAMCORE group at USC • Airport security • Where should checkpoints, canine units, etc. be deployed? • Deployed at LAX and another US airport, being evaluated for deployment at all US airports • Federal Air Marshals • Coast Guard • …

  3. Security example Terminal A Terminal B action action

  4. Security game A B A B

  5. Some of the questions raised D S D • Equilibrium selection? • How should we model temporal / information structure? • What structure should utility functions have? • Do our algorithms scale? S

  6. Observing the defender’s distribution in security Terminal A Terminal B observe Mo Sa Tu Th Fr We This model is not uncontroversial… [Pita, Jain, Tambe, Ordóñez, Kraus AIJ’10; Korzhyk, Yin, Kiekintveld, Conitzer, Tambe JAIR’11; Korzhyk, Conitzer, Parr AAMAS’11]

  7. Other nice properties of commitment to mixed strategies • Agrees w. Nash in zero-sum games • Leader’s payoff at least as good as any Nash eq. or even correlated eq. (von Stengel & Zamir [GEB ‘10]; see also Conitzer & Korzhyk [AAAI ‘11], Letchford, Korzhyk, Conitzer [draft]) ≥ • Noequilibrium selection problem

  8. Discussion about appropriateness of leadership model in security applications • Mixed strategy not actually communicated • Observability of mixed strategies? • Imperfect observation? • Does it matter much (close to zero-sum anyway)? • Modeling follower payoffs? • Sensitivity to modeling mistakes • Human players… [Pita et al. 2009]

  9. Example security game • 3 airport terminals to defend (A, B, C) • Defender can place checkpoints at 2 of them • Attacker can attack any 1 terminal A B C {A, B} {A, C} {B, C}

  10. Security resource allocation games[Kiekintveld, Jain, Tsai, Pita, Ordóñez, Tambe AAMAS’09] • Set of targets T • Set of security resources W available to the defender (leader) • Set of schedules • Resource w can be assigned to one of the schedules in • Attacker (follower) chooses one target to attack • Utilities: if the attacked target is defended, otherwise t1 s1 t3 w 1 t2 s2 t5 w 2 t4 s3

  11. Game-theoretic properties of security resource allocation games [Korzhyk, Yin, Kiekintveld, Conitzer, Tambe JAIR’11] For the defender: Stackelberg strategies are also Nash strategies minor assumption needed not true with multiple attacks • Interchangeability property for Nash equilibria (“solvable”) • no equilibrium selection problem • still true with multiple attacks [Korzhyk, Conitzer, Parr IJCAI’11]

  12. Compact LP • Cf. ERASER-C algorithm by Kiekintveld et al. [2009] • Separate LP for every possible t* attacked: Defender utility Marginal probability of t* being defended (?) Distributional constraints Attacker optimality Slide 11

  13. Counter-example to the compact LP w2 .5 .5 • LP suggests that we can cover every target with probability 1… • … but in fact we can cover at most 3 targets at a time .5 t t w1 t t .5 Slide 12

  14. Will the compact LP work for homogeneous resources? • Suppose that every resource can be assigned to any schedule. • We can still find a counter-example for this case: t t .5 .5 .5 .5 t t t t .5 .5 r r r 3 homogeneous resources

  15. Birkhoff-von Neumann theorem • Every doubly stochasticn x n matrix can be represented as a convex combination of n x n permutation matrices • Decomposition can be found in polynomial time O(n4.5), and the size is O(n2) [Dulmage and Halperin, 1955] • Can be extended to rectangular doubly substochastic matrices = .1 +.1 +.5 +.3 Slide 14

  16. Schedules of size 1 using BvN .7 w 1 t1 .2 .1 t2 .3 w 2 .7 t3 .1 .2 .2 .5

  17. Algorithms & complexity[Korzhyk, Conitzer, Parr AAAI’10] NP-hard (SAT) P (BvN theorem) NP-hard P (constraint generation) NP-hard NP-hard (3-COVER) Slide 16

  18. Placing checkpoints in a city [Tsai, Yin, Kwak, Kempe, Kiekintveld, Tambe AAAI’10; Jain, Korzhyk, Vaněk, Conitzer, Pěchouček, Tambe AAMAS’11]

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