Game Theory Explorer - Software for the Applied Game Theorist - PowerPoint PPT Presentation

Purpose Usage Client/Server Algorithms Future Game Theory Explorer - Software for the Applied Game Theorist Bernhard von Stengel Department of Mathematics London School of Economics July 2013 1

Purpose Usage Client/Server Algorithms Future Overview Explain and demonstrate GTE (Game Theory Explorer), open-source software, under development , for creating and analyzing non-cooperative games II l r I 2 1 T I 5 3 in strategic form: 3 4 B B T 6 4 II l r l r and extensive form: 5 3 6 4 2 1 3 4 2

Purpose Usage Client/Server Algorithms Future Intended users Applied game theorists: • experimental economists (analyze game before running experiment) • game-theoretic modelers in biology, political science, . . . • in general: non-experts in equilibrium analysis ⇒ design goal: ease of use Researchers in game theory: • testing conjectures about equilibria • as contributors: designers of game theory algorithms 3

Purpose Usage Client/Server Algorithms Future History: Gambit GTE now part of the Gambit open-source software development, http://www.gambit-project.org 2011 and 2012 supported by Google Summer of Code (GSoC) Gambit software started ∼ 1990 with Richard McKelvey (Caltech) to analyze games for experiments , developed since 1994 with Andy McLennan into C++ package, since 2001 maintained by Ted Turocy (Norwich, UK). • Gambit must be installed on PC/Mac/Linux, with GUI (graphical user interface) using platform-independent wxWidget • has collection of algorithms for computing Nash equilibria • offers scripting language , now developed using Python 4

Purpose Usage Client/Server Algorithms Future Features of GTE GTE independent browser-based development: • no software installation needed, low barrier to entry • nicer GUI than Gambit • export to graphical formats 5

Purpose Usage Client/Server Algorithms Future Features of GTE GTE independent browser-based development: • no software installation needed, low barrier to entry • nicer GUI than Gambit • export to graphical formats Disadvantages: • manual storing / loading of files for security reasons • long computations require local server installation (same GUI) 5

Purpose Usage Client/Server Algorithms Future Features of GTE GTE independent browser-based development: • no software installation needed, low barrier to entry • nicer GUI than Gambit • export to graphical formats Disadvantages: • manual storing / loading of files for security reasons • long computations require local server installation (same GUI) Contributors: David Avis ( lrs ), Rahul Savani (PhD 2006), Mark Egesdal (2011), Alfonso Gomez-Jordana, Martin Prause ( GSoC 2011, 2012 ) 5

Purpose Usage Client/Server Algorithms Future Example of a game 2 × 2 game in strategic form: II l r I 2 1 T 5 3 3 4 B 6 4 6

Purpose Usage Client/Server Algorithms Future Example of a game 2 × 2 game in strategic form: II l r I 2 1 T 5 3 3 4 B 6 4 with pure best responses 6

Purpose Usage Client/Server Algorithms Future Example of a game 2 × 2 game in strategic form: 0 1 II l r I 2 1 0 T 5 3 3 4 1 B 6 4 with pure best responses and equilibrium probabilities 6

Purpose Usage Client/Server Algorithms Future Extensive (= tree) form of the game Players move sequentially, information sets show lack of information about game state: I T B II l r l r 5 3 6 4 2 1 3 4 7

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I T B II II r a b l 5 3 6 4 2 1 3 4 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I T B II II r a b l 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II T B l−a l−b r−a r−b I II II 2 2 1 1 T 5 5 3 3 r a b l 3 4 3 4 B 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II T B l−a l−b r−a r−b I II II 2 2 1 1 T 5 5 3 3 r a b l 3 4 3 4 B 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II 0 1 0 0 T B l−a l−b r−a r−b I II II 2 2 1 1 1 T 5 5 3 3 r a b l 3 4 3 4 B 0 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II 1 0 0 0 T B l−a l−b r−a r−b I II II 2 2 1 1 0 T 5 5 3 3 l r a b 3 4 3 4 1 B 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) Other equilibria: ( B , r - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II 0 1/2 0 1/2 T B l−a l−b r−a r−b I II II 2 2 1 1 T 0 5 5 3 3 a b l r 3 4 3 4 1 B 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) Other equilibria: ( B , r - b ) , ( B , 1 2 l - b 1 2 r - b ) 8

Purpose Usage Client/Server Algorithms Future Commitment (leadership) game Changed game when player I can commit: I II 1/2 1/2 0 0 T B l−a l−b r−a r−b I II II 2 2 1 1 T 1 5 5 3 3 a b l r 3 4 3 4 0 B 6 4 6 4 5 3 6 4 2 1 3 4 Subgame perfect equilibrium: ( T , l - b ) Other equilibria: ( B , r - b ) , ( B , 1 2 l - b 1 2 r - b ) , ( T , 1 2 l - a 1 2 l - b ) 8

Purpose Usage Client/Server Algorithms Future GTE output for the commitment game 9

Purpose Usage Client/Server Algorithms Future Demonstration of GTE Preceding games: • 2 × 2 game in strategic form • extensive form of that game • commitment game, extensive and strategic form 10

Purpose Usage Client/Server Algorithms Future Demonstration of GTE Preceding games: • 2 × 2 game in strategic form • extensive form of that game • commitment game, extensive and strategic form Next: create from scratch a more complicated extensive game • imperfectly observable commitment 10

Purpose Usage Client/Server Algorithms Future Game with imperfectly observable commitment I B T 99/100 99/100 1/100 1/100 II l r l r 5 3 6 4 2 1 3 4 II a b a b 5 3 6 4 2 1 3 4 11

Purpose Usage Client/Server Algorithms Future Game tree drawn left to right 5 , 2 l 99/100 r 3 , 1 1/100 T 5 , 2 a II I b 3 1 , 6 , 3 l B 1/100 II r 4 , 4 99/100 6 , 3 a b 4 , 4 12

Purpose Usage Client/Server Algorithms Future GTE output for imperfectly observable commitment 13

Purpose Usage Client/Server Algorithms Future More complicated signaling game, 5 equilibria 1/2 1/2 1 1 Yi Ni Yn Nn 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 −4 0 −1 0 1 0 0 0 2 yifY nifY yifY nifY 10 −2 −3 0 10 −5 −2 −1 2 yifN nifN yifN nifN 8 −1 −2 0 5 −3 −3 −1 14

Purpose Usage Client/Server Algorithms Future Some more strategic-form games For studying more complicated games: generate game matrices as text files, copy and paste into strategic-form input. Future extension: Automatic generation via command lines or “worksheets” for scripting, connection with Python and Gambit 15

Purpose Usage Client/Server Algorithms Future GTE software architecture Client (your computer with a browser): • GUI: JavaScript (Flash’s variant called ActionScript) • store and load game described in XML format • export to graphic formats (.png or XFIG → EPS, PDF) • for algorithm: send XML game description to server 16

Purpose Usage Client/Server Algorithms Future GTE software architecture Client (your computer with a browser): • GUI: JavaScript (Flash’s variant called ActionScript) • store and load game described in XML format • export to graphic formats (.png or XFIG → EPS, PDF) • for algorithm: send XML game description to server Server (hosting client program and equilibrium solvers): • converts XML to Java data structure (similar to GUI) • solution algorithms as binaries (e.g. C program lrs ), send results as text back to client ⇒ cannot use restrictive public servers like “Google App Engine” 16

Purpose Usage Client/Server Algorithms Future High usage of computation resources Finding all equilibria takes exponential time ⇒ for large games, server should run on your computer, not a public one achieved by local server installation (“Jetty”), requires installation, but offers same user interface. 17