slides-SIT2-article - F. Koessler / November 12, 2008 Cheap...

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Unformatted text preview: F. Koessler / November 12, 2008 Cheap Talk Games: Extensions 1/ Cheap Talk Games: Extensions Outline (November 12, 2008) • The Art of Conversation: Multistage Communication and Compromises • Mediated Communication: Correlated and Communication Equilibria 2/ 1 The Art of Conversation: Multistage Communication and Compromises Aumann et al. (1968): Allowing more than one communication stage can extend and Pareto improve the set of Nash equilibria, even if only one player is privately informed Aumann and Hart (2003, Ecta): Full characterization of equilibrium payoffs induced by multistage cheap talk communication in finite two-player games with incomplete information on one side Multistage communication also extends the equilibrium outcomes in the classical model of Crawford and Sobel (1982) F. Koessler / November 12, 2008 Cheap Talk Games: Extensions 3/ 1.1 Examples Example. (Compromising) L R T 6 , 2 , B , 2 , 6 Jointly controlled lottery (JCL): b a 1 2 b L R 6 , 2 , , 2 , 6 a L R T 6 , 2 , B , 2 , 6 b L R 6 , 2 , , 2 , 6 a L R 6 , 2 , , 2 , 6 1 2 a + 1 2 b ⇒ 1 2 ( T, L ) + 1 2 ( B,R ) → (4 , 4) 4/ Example. (Signalling, and then compromising) k 1 L M R T (6 , 2) (0 , 0) (3 , 0) B (0 , 0) (2 , 6) (3 , 0) k 2 L M R T (0 , 0) (0 , 0) (4 , 4) B (0 , 0) (0 , 0) (4 , 4) Interim equilibrium payoffs ((4 , 4) , 4) The two communication stages cannot be reversed (compromising should come after signalling) F. Koessler / November 12, 2008 Cheap Talk Games: Extensions 5/ Example. (Compromising, and then signaling) (Example 5) j 1 j 2 j 3 j 4 j 5 k 1 1 , 10 3 , 8 , 5 3 , 1 , − 8 p k 2 1 , − 8 3 , , 5 3 , 8 1 , 10 1 − p Interim equilibrium payoffs ((2 , 2) , 8) = 1 2 ((3 , 3) , 6) + 1 2 ((1 , 1) , 10) Of course, the two communication stages cannot be reversed (the compromise determines the type of signalling) 6/ Example. (Signalling, then compromising, and then signalling) j 1 j 2 j 3 j 4 j 5 j 6 k 1 1 , 10 3 , 8 , 5 3 , 1 , − 8 2 , 1 / 3 k 2 1 , − 8 3 , , 5 3 , 8 1 , 10 2 , 1 / 3 k 3 , , , , , 2 , 8 1 / 3 Interim equilibrium payoffs ((2 , 2 , 2) , 8) F. Koessler / November 12, 2008 Cheap Talk Games: Extensions 7/ 1.2 Multistage and Bilateral Cheap Talk Game Γ n ( p ) Bilateral communication: the uninformed player can also send messages Player 1: informed, expert Player 2: uninformed, decision maker K : set of information states (i.e., types) of P1, probability distribution p J : set of actions of P2 P1’s payoff is A k ( j ) and P2’s payoff is B k ( j ) M 1 : set of messages of the expert (independent of his type) M 2 : set of message of the decisionmaker 8/ At every stage t = 1 ,...,n , P1 sends a message m 1 t ∈ M 1 to P2 and, simultaneously, P2 sends a message m 2 t ∈ M 2 to P1 At stage n + 1 , P2 chooses j in J Information Phase Expert learns k ∈ K Communication Phase Expert and DM send ( m 1 t ,m 2 t ) ∈ M 1 × M 2 ( t = 1 ,...n ) Action Phase DM chooses j ∈ J F. Koessler / November 12, 2008 Cheap Talk Games: Extensions 9/ 1.31....
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This note was uploaded on 01/23/2011 for the course ECONOMICS gt512 taught by Professor Breviart during the Spring '10 term at Télécom Paris.

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slides-SIT2-article - F. Koessler / November 12, 2008 Cheap...

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