1 What is Game Theory? Game Theory 1. Introduction. Rational Agents. Rational Agents in Game Theory
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1 Theory. Inroducion Alber-Ludwig-Univeriä Freiburg Bernhard Nebel and Rober Mamüller Summer emeer 208 SS 208 B. Nebel, R. Mamüller Theory 3 / 23 Raional Agen Raional Agen in Theory Conider raionally acing agen: Siuaion in game heory: ac agen world oberve Raional agen maximize heir (expeced) uiliy: deciion heory Markov deciion procee (MDP) reinforcemen learning AI planning... SS 208 B. Nebel, R. Mamüller Theory 4 / 23 SS 208 B. Nebel, R. Mamüller Theory 5 / 23
2 Raional Agen in Theory Hiory of Theory Muliple raional agen ineracing in raegic deciion iuaion. reuling uiliy depend on wha oher agen do. all agen know ha oher agen are raional (hi i even common knowledge). Inereing queion: how o model uch raegic iuaion how o olve uch raegic iuaion originally par of mahemaic and heoreical economic oday ubiquiou here: arificial inelligence and compuer cience perpecive raionaliy aumpion ( homo economicu ) more warraned for arificial agen han for human inereing algorihmic queion how o deign game ha have deired oluion heory i he udy and analyi of uch raegic deciion iuaion. SS 208 B. Nebel, R. Mamüller Theory 6 / 23 SS 208 B. Nebel, R. Mamüller Theory 7 / 23 2 Board and Card Two-player board and card game: very pecial whaever i good for one player i bad for he oher (ricly compeiive game) recen viible ucce: Poker (no-limi, head-up, hold em) SS 208 B. Nebel, R. Mamüller Theory 9 / 23 SS 208 B. Nebel, R. Mamüller Theory 0 / 23
3 Aucion Congeion Aucion: Think of ebay, Google AdWord,... eing: one objec hould be allocaed o one ou of a number of bidder. queion: wha bidding proocol o ue? who i he winner? wha doe he winning bidder have o pay? Queion: Aume ha here are n = 2 agen. Which roue will hey chooe? Average ravel co per agen:? SS 208 B. Nebel, R. Mamüller Theory / 23 SS 208 B. Nebel, R. Mamüller Theory 2 / 23 Congeion Congeion oher agen one agen 0 Queion: Aume ha here are n = 2 agen. Which roue will hey chooe? Average ravel co per agen:.5 Queion: Aume ha here are n = 2 agen. Which roue will hey chooe now (wih free new road)? Average ravel co per agen:? SS 208 B. Nebel, R. Mamüller Theory 2 / 23 SS 208 B. Nebel, R. Mamüller Theory 2 / 23
4 Congeion Securiy boh agen 0 Queion: Aume ha here are n = 2 agen. Which roue will hey chooe now (wih free new road)? Securiy game: eing: a faciliy (e. g., an airpor) ha o be guarded o avoid aack poible mehod: vii all criical place chooe he place probabiliically find a probabiliy diribuion for he rouing ha minimize expeced damage even under he aumpion ha he aacker can oberve he guard Average ravel co per agen: 2 >.5 SS 208 B. Nebel, R. Mamüller Theory 2 / 23 SS 208 B. Nebel, R. Mamüller Theory 3 / 23 Elecion 3 eing: a e of alernaive (candidae) and a e of voer, deermine winner or ranking queion: wha queion o ak? how o deermine a winner / ranking? wha i he compuaional complexiy of deermining a winner? can he proocol be made manipulaion-afe? SS 208 B. Nebel, R. Mamüller Theory 4 / 23 SS 208 B. Nebel, R. Mamüller Theory 6 / 23
5 4 : General aumpion: All player wan o maximize heir own uiliy and nohing ele. Conra: Alruiic agen wan o maximize uiliy of oher agen Cooperaive agen wan o maximize group uiliy Byzanine agen wan o minimize uiliy of oher agen Limiaion: agen may no foreee all conequence of heir deciion (bounded raionaliy) agen may no know all relevan informaion abou he game rucure (incomplee informaion) agen may no know all relevan informaion abou he curren ae of he game (imperfec informaion) SS 208 B. Nebel, R. Mamüller Theory 7 / 23 SS 208 B. Nebel, R. Mamüller Theory 9 / 23 5 raegic game exenive game repeaed game imperfec informaion game and Poker ocial choice heory mechanim deign SS 208 B. Nebel, R. Mamüller Theory 20 / 23 SS 208 B. Nebel, R. Mamüller Theory 22 / 23
6 Beauy Cone We play a game called Beauy Cone. Rule Everybody chooe a naural number n wih n 00. The player ha come cloe o 2 /3 of he average win. Now i your urn! SS 208 B. Nebel, R. Mamüller Theory 23 / 23
Game Theory. 1. Introduction. Bernhard Nebel and Robert Mattmüller. Summer semester Albert-Ludwigs-Universität Freiburg
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