This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECON 401: Game theory: solution concepts Siyang Xiong Rice University October 27, 2011 Xiong (Rice University) ECON 401 October 27, 2011 1 / 13 mixed strategies: normalform games for any game (normalform or extensiveform), suppose S i is the set of strategies available to player i . A mixed strategy is a probability over S i . a mixed strategy is denoted by & i 24 . S i / . for example: prisoner&s dilemma: don&t confess confess don&t confess & 2 , & 2 & 10 , & 1 confess & 1 , & 10 & 5 , & 5 a mixed strategy & 1 : [with probability 2 3 , take [ don&t confess ] , and with probability 1 3 , take [ confess ] ], denoted by 2 3 [ don&t confess ] C 1 3 [ confess ] . a mixed strategy & 2 : [with probability 1 4 , take [ don&t confess ] , and with probability 3 4 , take [ confess ] ], denoted by 1 4 [ don&t confess ] C 3 4 [ confess ] . Xiong (Rice University) ECON 401 October 27, 2011 2 / 13 with players taking mixed strategy, their returns in this game are the expected payo/s induced by the mixed strategies: suppose player 1 takes & 1 and player 2 takes & 2 , then player 1 gets 2 3 1 4 U 1 [ don&t confess , don&t confess ] C 2 3 3 4 U 1 [ don&t confess , confess ] C 1 3 1 4 U 1 [ confess , don&t confess ] C 1 3 3 4 U 1 [ confess , confess ] D 1 6 . & 2 / C 1 2 . & 10 / C 1 12 . & 1 / C 1 4 . & 5 / D & 4 & 60 & 1 & 15 12 D& 80 12 D& 20 3 player 2 gets 2 3 1 4 U 2 [ don&t confess , don&t confess ] C 2 3 3 4 U 2 [ don&t confess , confess ] C 1 3 1 4 U 2 [ confess , don&t confess ] C 1 3 3 4 U 2 [ confess...
View Full
Document
 Spring '11
 Siyang
 Economics, Game Theory

Click to edit the document details