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PENG Session 1 Roland M uhlenbernd Seminar f ur - - PowerPoint PPT Presentation
PENG Session 1 Roland M uhlenbernd Seminar f ur - - PowerPoint PPT Presentation
PENG Session 1 Roland M uhlenbernd Seminar f ur Sprachwissenschaft University of T ubingen Introduction Roland M uhlenbernd Email: roland.muehlenbernd@uni-tuebingen.de Room 1.24 (Wilhelmstr. 19) w 3
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Introduction: Course Info
◮ Time: Thursday 12-14 ◮ Place: Wilhelmstr. 19, 2.26 ◮ Tasks
◮ Teamwork! Group Coordination, Time Management, Data
Management (e.g. SVN), Internet Platform
◮ Programming Project: MAS, Games, Simulation, Language
Evolution
◮ Paperwork: Final Article, Documentation
◮ Assessment: Individual Treatment ◮ Planed Schedule - Big Picture:
Topic Weeks Timeframe Completion Introduction 3 Oct 20 - Nov 3 Tournament Programming 7 Nov 4 - Dec 22 Presentation Paperwork 4 Jan 5 - Feb 2 Subchapters
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Games: Classics & Solutions
C D C 3, 3 0, 5 D 5, 0 1, 1
C: Cooperate, D: Defect
W G W 2, 2
- 1, 5
G
5,-1
0, 0
W: Work Hard, G: Goof Off
S R S 2, 2 0, 1 R 1, 0 1, 1
S: Stag, R: Rabbit
B S B 2, 1 0, 0 S 0, 0 1, 2
B: Bach, S: Stravinsky
L R L
- 1,1
1,-1
R
1,-1
- 1,1
L: Left, R: Right
P V P 1, 1 0, 0 V 0, 0 1, 1
P: Paris, V: Vienna
Solutions:
◮ (strict) Nash equilibria? ◮ Pareto optimality? ◮ Risk dominance?
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Games: Signaling Game
◮ a signaling game is a tuple SG = {S, R}, T, Pr, M, A, U ◮ a Lewis game is defined by: ◮ T = {t1, t2} ◮ M = {m1, m2} ◮ A = {a1, a2} ◮ Pr(t1) = Pr(t2) = .5 ◮ U(ti, aj) =
1 if i = j else a1 a2 t1 1 t2 1 N S R 1 R 1 S R 1 R 1
.5 .5
t1 t2 m1 m2 m1 m2 a1 a2 a1 a2 a1 a2 a1 a2
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Games: Signaling Game Strategies
Sender & Receiver Strategies: σ1:
t1 m1 t2 m2
σ2:
t1 m2 t2 m1
σ3:
t1 m1 t2 m2
σ4:
t1 m2 t2 m1
ρ1:
m1 a1 m2 a2
ρ2:
m1 a2 m2 a1
ρ3:
m1 a1 m2 a2
ρ4:
m1 a2 m2 a1
Expected utilities: ρ1 ρ2 ρ3 ρ4 σ1 1 .5 .5 σ2 1 .5 .5 σ3 .5 .5 .5 .5 σ4 .5 .5 .5 .5 Signaling Languages: L1: t1 t2 m1 m2 a1 a2 L2: t1 t2 m1 m2 a1 a2
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