Lect14_Slides

Lect14_Slides - Complete vs. Incomplete Information Games...

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Complete vs. Incomplete Information Games All games can be classified as complete information games or incomplete information games . l t i f t i l h t it i t Complete information games – the player whose turn it is to move knows at least as much as those who moved before him/her. Complete information games include: Perfect information games –players know the full history of the game, all moves made by all players etc and all payoffs e.g. an extensive form game without any information sets. Imperfect information games – games involving simultaneous moves where players know all the possible outcomes/payoffs, but not the actions chosen by other players. yp y Incomplete information games: At some node in the game the player whose turn it is to make a choice knows less than a player ho has already moved Also called ayesian games who has already moved. Also called Bayesian games.
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Imperfect vs. Incomplete Information Games •I n a game of imperfect information, players are gp , p y simply unaware of the actions chosen by other players. However they know who the other players e hat their possible strategies/actions are and are, what their possible strategies/actions are, and the preferences/payoffs of these other players. Hence, information about the other players in imperfect information is complete. n incomplete information games, players may or may not know some information about the other players, e.g. their “type”, their strategies, payoffs r their preferences. o t e peee ces .
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Example 1a of an Incomplete Information Game • Prisoner’s Dilemma Game. Player 1 has the standard selfish preferences but Player 2 has either selfish preferences or nice preferences. layer 2 knows her type, but Player 1 does not know 2’s type Player 2 knows her type, but Player 1 does not know 2s type C D C D ,4 ,6 ,6 ,4 22 C D 4,4 0,6 C D 4,6 0,4 6,0 2,2 6,2 2,0 Player 2 selfish Player 2 nice 11 • Recall that C=cooperate, D=defect. If player 2 is selfish then player 1 will want to choose D, but if player 2 is nice, player y y 1’s best response is still to choose D, since D is a dominant strategy for player 1 in this incomplete information game.
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Example 1b of an Incomplete Information Game • Prisoner’s Dilemma Game. Player 1 has the standard selfish preferences but Player 2 has either selfish preferences or nice preferences. Suppose player 1’s preferences now depend on hether player 2 is nice or selfish (or vice versa) whether player 2 is nice or selfish (or vice versa). C D C D ,4 ,6 ,6 ,4 22 C D 4,4 0,6 C D 6,6 2,4 6,0 2,2 4,2 0,0 Player 2 selfish Player 2 nice 11 • If 2 is selfish then player 1 will want to be selfish and choose D, but if player 2 is nice, player 1’s best response is to play C! y y Be nicer to those who play nice, mean to those who play mean.
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Example 1b in Extensive Form, Where Player 2’s Type is Due to “Nature” Information Set Prevents 1 From Knowing 2’s Type and 2’s Move
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xample 1b Again, But With a Higher Example 1b Again, But With a Higher Probability that Type 2 is Selfish
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Analysis of Example 1b
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This note was uploaded on 12/26/2011 for the course ECON 171 taught by Professor Charness,g during the Fall '08 term at UCSB.

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Lect14_Slides - Complete vs. Incomplete Information Games...

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