STV: Model Checking for Strategies under Imperfect Information - - PowerPoint PPT Presentation

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STV: Model Checking for Strategies under Imperfect Information - - PowerPoint PPT Presentation

Jan 13, 2023 675 likes •1.01k views

STV: Model Checking for Strategies under Imperfect Information Damian Kurpiewski Institute of Computer Science Polish Academy of Sciences (joint work with Wojtek Jamroga and Micha Knapik) LAMAS, 09/05/2020 Outline 2 / 1 Outline 3 / 1

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STV: Model Checking for Strategies under Imperfect Information

Damian Kurpiewski

Institute of Computer Science Polish Academy of Sciences (joint work with Wojtek Jamroga and Michał Knapik)

LAMAS, 09/05/2020

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SLIDE 2

Outline

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SLIDE 3

Outline

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ATL: What Agents Can Achieve

  • ATL: Alternating-time Temporal Logic [Alur et al. 1997-2002]
  • Temporal logic meets game theory
  • Main idea: cooperation modalities
  • A

Φ: coalition A has a collective strategy to enforce Φ ❀ Φ can include temporal operators: X (next), F (sometime in the future), G (always in the future), U (strong until)

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ATL with incomplete information

  • Imperfect information (q ∼a q′)

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ATL with incomplete information

  • Imperfect information (q ∼a q′)
  • Imperfect recall - agent memory coded within state of the model

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ATL with incomplete information

  • Imperfect information (q ∼a q′)
  • Imperfect recall - agent memory coded within state of the model
  • Uniform strategies - specify same choices for indistinguishable states:

q ∼a q′ = ⇒ sa(q) = sa(q′)

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ATL with incomplete information

  • Imperfect information (q ∼a q′)
  • Imperfect recall - agent memory coded within state of the model
  • Uniform strategies - specify same choices for indistinguishable states:

q ∼a q′ = ⇒ sa(q) = sa(q′)

  • Fixpoint equivalences do not hold anymore

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SLIDE 9

ATL with incomplete information

  • Imperfect information (q ∼a q′)
  • Imperfect recall - agent memory coded within state of the model
  • Uniform strategies - specify same choices for indistinguishable states:

q ∼a q′ = ⇒ sa(q) = sa(q′)

  • Fixpoint equivalences do not hold anymore
  • Model checking ATLir is ∆p

2-complete

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Example - Simple Model of Voting and Coercion

q0 q1

votei,1

q2

votei,2

q3

votei,1

q4

votei,1

q5

votei,2

q6

votei,2

q7

finishi votei,1

q8

finishi votei,1 puni

q9

finishi votei,1

q10

finishi votei,1 puni

q11

finishi votei,2 puni

q12

finishi votei,2

q13

finishi votei,2 puni

q14

finishi votei,2

(vote1, −) (vote2, −) ( g i v e , − ) (ng, −) ( g i v e , − ) (ng, −) ( − , n p ) (−, pun) ( − , n p ) (−, pun) ( − , n p ) (−, pun) ( − , n p ) (−, pun)

c c c c

(wait, −) (wait, −) (wait, −)

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Example Formulae

coercer F(¬pun1 ∨ vote1,1): “Coercer can coerce Voter to vote for first candidate”

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Example Formulae

coercer F(¬pun1 ∨ vote1,1): “Coercer can coerce Voter to vote for first candidate” FALSE

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Example Formulae

coercer F(¬pun1 ∨ vote1,1): “Coercer can coerce Voter to vote for first candidate” FALSE

voter1 G(¬pun1 ∧ ¬vote1,1): “Voter can avoid punishment without voting for first candidate”

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Example Formulae

coercer F(¬pun1 ∨ vote1,1): “Coercer can coerce Voter to vote for first candidate” FALSE

voter1 G(¬pun1 ∧ ¬vote1,1): “Voter can avoid punishment without voting for first candidate” TRUE

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Outline

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Approximate Verification of Strategic Ability M | =ir ϕ : DIFFICULT!

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Approximate Verification of Strategic Ability M | =ir ϕ : DIFFICULT!

M | =ir ϕ M | = LB(ϕ) M | = UB(ϕ)

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Approximate Verification of Strategic Ability M | =ir ϕ : DIFFICULT!

M | =ir ϕ M | = LB(ϕ) M | = UB(ϕ) perfect information

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Approximate Verification of Strategic Ability M | =ir ϕ : DIFFICULT!

M | =ir ϕ M | = LB(ϕ) M | = UB(ϕ) perfect information

  • ur contribution
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SLIDE 20

Approximate Verification of Strategic Ability M | =ir ϕ : DIFFICULT!

M | =ir ϕ M | = LB(ϕ) M | = UB(ϕ) perfect information

  • ur contribution

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Domino DFS

q0 start q2 q1 q4 p q3 p q5 ¬p (A, U) (B, ⋆) (A, V) (A, V) (A, U) (B, ⋆) (B, ⋆) (A, U) (A, V) 1

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Domino DFS

q0 start q2 q1 q4 p q3 p q5 ¬p (A, U) (B, ⋆) (A, V) (A, V) (A, U) (B, ⋆) (B, ⋆) (A, U) (A, V) 1

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Domino DFS

q0 start q2 q1 q4 p q3 p q5 ¬p (A, U) (B, ⋆) (A, V) (A, V) (A, U) (B, ⋆) (B, ⋆) (A, U) (A, V) 1

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Domino DFS

q0 start q2 q1 q4 p q3 p q5 ¬p (A, U) (B, ⋆) (A, V) (A, V) (A, U) (B, ⋆) (B, ⋆) (A, U) (A, V) 1

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Domino DFS

q0 start q2 q1 q4 p q3 p q5 ¬p (A, U) (B, ⋆) (A, V) (A, V) (A, U) (B, ⋆) (B, ⋆) (A, U) (A, V) 1

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Outline

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Implemented models

  • Bridge scenario
  • Castles
  • TianJi
  • Drones
  • Simple Voting

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Bridge scenario

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Bridge scenario

  • Typical bridge play scenario, modified by two variables: n, k
  • Each player holds k cards in hand
  • Deck consists of 4n cards in total
  • We consider only endplay
  • Random deal
  • Four players - S, W, N, E
  • Declarer (S) handles his own cards and the ones of the dummy (N)
  • Players remember already played cards
  • Everyone see dummy cards
  • NoTrump contract

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DEMO

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Experimental results - Bridge scenario

Conf. DominoDFS MCMAS Approx.

  • Approx. opt.

(1, 1) 0.0006 0.12 0.0008 < 0.0001 (2, 2) 0.01 8712∗ 0.01 < 0.0001 (3, 3) 0.8 timeout 0.8 0.06 (4, 4) 160 timeout 384 5.5 (5, 5)∗ 1373 timeout 8951 39 (5, 5) memout timeout memout 138 (6, 6)∗ memout timeout memout 4524

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Experimental results - Castles

Conf. DominoDFS MCMAS SMC (1, 1, 1) 0.3 65 63 (2, 1, 1) 1.5 12898 184 (3, 1, 1) 25 timeout 6731 (2, 2, 1) 25 timeout 4923 (2, 2, 2) 160 timeout timeout (3, 2, 2) 2688 timeout timeout (3, 3, 2) timeout timeout timeout

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THANK YOU

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