Tutorial9

Tutorial9 - CSC5350 Game Theory in Computer Science...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
CSC5350 Game Theory in Computer Science Tutorial 9 Chen Wenhao whchen@cse.cuhk.edu.hk SHB 905
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline ± Beliefs ± Assessment ± Sequential equilibrium ± Coalitional Games ± Feasible payoff and Core
Background image of page 2
Beliefs ± At an information set that contains more than one history ± player whose turn it is to move forms a belief about e history that has occurred the history that has occurred ± the belief is modeled as a probability distribution over the histories in the information set ± At an information set containing a single history ± the only possible belief assigns probability 1 to that history ± A collection on beliefs, one for each information set of every player, is called a belief system
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Assessment ± An assessment consists of ± A profile of behavioral strategies belief system ± A belief system
Background image of page 4
Sequential equilibrium ± An assessment is a sequential equilibrium if it satisfies the following two requirements ± equential rationality Sequential rationality ± Each player s strategy is optimal whenever she has to move, given her belief and the other players strategies ± Consistency of beliefs with strategies ± Each player s belief is consistent with the strategy profile
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Find the set of sequential equilibrium of the following game 1 L M R 2 1, 1 1 0 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 6
Example 1 ± Let player 1 s behavioral strategy = (a, b, c) 1 L M R a b c 2 1, 1 1 0 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Case 1 b > c ase 2 ± Case 2 b< c ± Case 3 b= c> 0 ± Case 4 b= c= 0
Background image of page 8
Example 1 ± Case 1 b > c 1 L M R a b c 2 1, 1 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Case 1 b > c 1 L M R a b c 2 1, 1 0 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 10
Example 1 ± Case 1 b > c 1 L M R a b c 2 1 , 1 1 0 0 1 3 , 1 -2, 0 2 , 0 -1, 1
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Case 1 b > c 1 L M R a b c 2 1, 1 1 0 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 12
Example 1 ± Case 1 b > c ± Player 2 chooses L ence 1 ± Hence b = 1 ± (M, L) is a sequential equilibrium
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Case 2 b < c 1 L M R a b c 2 1, 1 1 0 3, 1 -2, 0 2, 0 -1, 1
Background image of page 14
Example 1 ± Case 2 b < c 1 L M R a b c 2 1, 1 1 0 0 3, 1 -2, 0 2, 0 -1, 1
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 1 ± Case 2 b < c 1 L M R a b c 2 1 , 1 1 0 0 1 3, 1 -2 , 0 2, 0 -1 , 1
Background image of page 16
Example 1 ± Case 2 b < c 1 = =0 L M R a b c b c 0 contradiction 2 1 , 1 1 0 0 1 3, 1 -2, 0 2, 0 -1, 1
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/23/2010 for the course CSC CSC5350 taught by Professor Leunghofung during the Winter '09 term at CUHK.

Page1 / 34

Tutorial9 - CSC5350 Game Theory in Computer Science...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online