Tutorial9

# Tutorial9 - CSC5350 Game Theory in Computer Science...

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CSC5350 Game Theory in Computer Science Tutorial 9 Chen Wenhao whchen@cse.cuhk.edu.hk SHB 905

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Outline ± Beliefs ± Assessment ± Sequential equilibrium ± Coalitional Games ± Feasible payoff and Core
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

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Assessment ± An assessment consists of ± A profile of behavioral strategies belief system ± A belief system
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

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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
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

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Example 1 ± Case 1 b > c ase 2 ± Case 2 b< c ± Case 3 b= c> 0 ± Case 4 b= c= 0
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

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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
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

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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
Example 1 ± Case 1 b > c ± Player 2 chooses L ence 1 ± Hence b = 1 ± (M, L) is a sequential equilibrium

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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
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

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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
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

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

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Tutorial9 - CSC5350 Game Theory in Computer Science...

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