Unformatted text preview: is inversely proportional to the total size of the data, so that it takes x i Ï„ ( x 1 , . . . , x n ) minutes to send the message where Ï„ ( x 1 , . . . , x n ) = x 1 + Â· Â· Â· + x n . The payo f of student i is Î¸ i x i âˆ’ x i Ï„ ( x 1 , . . . , x n ) , where Î¸ i âˆˆ { 1 , 2 } is a payo f parameter of player i , privately known by himself or herself. For each j 6 = i , independent of Î¸ j , player j assigns probability 1/2 to Î¸ i = 1 and probability 1/2 to Î¸ i = 2 . Everything described so far is common knowledge. (a) Write this game formally as a Bayesian game. (b) Compute the symmetric Bayesian Nash equilibrium of this game. Hint: symmetric means that x i ( Î¸ i ) = x j ( Î¸ j ) when Î¸ i = Î¸ j . In the symmetric equilibrium one of the types will choose zero, i.e., for some Î¸ âˆˆ { 1 , 2 } , x i ( Î¸ i ) = whenever Î¸ i = Î¸ . The expected value E [ x 1 + Â· Â· Â· + x n ] of x 1 + Â· Â· Â· + x n is E [ x 1 ] + Â· Â· Â· + E [ x n ] . 1...
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 Spring '05
 MuhammadYildiz
 Game Theory

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