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 Π Room 1.24 (Wilhelmstr. 19) w 3 http://www2.sfs.uni-tuebingen.de/˜roland/PENG Introduce yourself...

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

Games: Classics & Solutions C D W G S R 3 , 3 0 , 5 2 , 2 0 , 1 C W 2 , 2 -1 , 5 S D 5 , 0 1 , 1 0 , 0 R 1 , 0 1 , 1 G 5 , -1 C: Cooperate, D: Defect W: Work Hard, G: Goof Off S: Stag, R: Rabbit B S L R P V B 2 , 1 0 , 0 L -1,1 1,-1 P 1 , 1 0 , 0 0 , 0 1 , 2 S R 1,-1 -1,1 V 0 , 0 1 , 1 B: Bach, S: Stravinsky L: Left, R: Right P: Paris, V: Vienna Solutions: ◮ (strict) Nash equilibria? ◮ Pareto optimality? ◮ Risk dominance?

Games: Signaling Game ◮ a signaling game is a tuple SG = �{ S , R } , T , Pr , M , A , U � ◮ a Lewis game is defined by: � 1 if i = j ◮ T = { t 1 , t 2 } ◮ U ( t i , a j ) = 0 else ◮ M = { m 1 , m 2 } a 1 a 2 ◮ A = { a 1 , a 2 } t 1 1 0 ◮ Pr ( t 1 ) = Pr ( t 2 ) = . 5 0 1 t 2 N t 1 t 2 . 5 . 5 S S m 1 m 2 m 1 m 2 R R R R a 1 a 2 a 1 a 2 a 1 a 2 a 1 a 2 1 0 1 0 0 1 0 1

Games: Signaling Game Strategies Sender & Receiver Strategies: t 1 m 1 t 1 m 1 t 1 m 1 t 1 m 1 σ 1 : σ 2 : σ 3 : σ 4 : m 2 m 2 m 2 m 2 t 2 t 2 t 2 t 2 m 1 a 1 m 1 a 1 m 1 a 1 m 1 a 1 ρ 1 : ρ 2 : ρ 3 : ρ 4 : a 2 m 2 a 2 m 2 a 2 m 2 a 2 m 2 Expected utilities: Signaling Languages: m 1 a 1 t 1 ρ 1 ρ 2 ρ 3 ρ 4 L 1 : 1 0 .5 .5 σ 1 m 2 a 2 t 2 0 1 .5 .5 σ 2 .5 .5 .5 .5 t 1 m 1 a 1 σ 3 L 2 : .5 .5 .5 .5 σ 4 m 2 a 2 t 2

Homework: The Evolution of Cooperation Read: ◮ Axelrod, R. (1984), ”The Evolution of Cooperation” (Chapter 1,2)