Lecture8 (1).pdf - EC3312 Game Theory and Applications to...

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EC3312 Game Theory and Applications to Economics Luo Xiao, Lecturer Department of Economics, National University of Singapore 23 March 2018 A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 1 / 16
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Static Bayesian Games static (= one-shot, simultaneous-move) A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 2 / 16
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Static Bayesian Games static (= one-shot, simultaneous-move) games of incomplete information (= Bayesian games ): at least one player does not know another player°s identity, e.g. payo/ function A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 2 / 16
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Static Bayesian Games static (= one-shot, simultaneous-move) games of incomplete information (= Bayesian games ): at least one player does not know another player°s identity, e.g. payo/ function Examples: Cournot competition under uncertainty, sealed-bid auctions A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 2 / 16
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Cournot Competition under Asymmetric Information Two ±rms choose their quantities q 1 and q 2 (of a homogeneous product) simultaneously. The market-clearing price is given by the inverse demand function P ( Q ) = a ° Q , where Q = q 1 + q 2 A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 3 / 16
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Cournot Competition under Asymmetric Information Two ±rms choose their quantities q 1 and q 2 (of a homogeneous product) simultaneously. The market-clearing price is given by the inverse demand function P ( Q ) = a ° Q , where Q = q 1 + q 2 Firm 1°s cost function is: C 1 ( q 1 ) = cq 1 , where c < a . Firm 2°s cost function is: C 2 ( q 2 ) = ° c H q 2 , with probability θ c L q 2 , with probability 1 ° θ , where c L < c H < a A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 3 / 16
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Cournot Competition under Asymmetric Information Two ±rms choose their quantities q 1 and q 2 (of a homogeneous product) simultaneously. The market-clearing price is given by the inverse demand function P ( Q ) = a ° Q , where Q = q 1 + q 2 Firm 1°s cost function is: C 1 ( q 1 ) = cq 1 , where c < a . Firm 2°s cost function is: C 2 ( q 2 ) = ° c H q 2 , with probability θ c L q 2 , with probability 1 ° θ , where c L < c H < a Information is asymmetric: A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 3 / 16
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Cournot Competition under Asymmetric Information Two ±rms choose their quantities q 1 and q 2 (of a homogeneous product) simultaneously. The market-clearing price is given by the inverse demand function P ( Q ) = a ° Q , where Q = q 1 + q 2 Firm 1°s cost function is: C 1 ( q 1 ) = cq 1 , where c < a . Firm 2°s cost function is: C 2 ( q 2 ) = ° c H q 2 , with probability θ c L q 2 , with probability 1 ° θ , where c L < c H < a Information is asymmetric: ±rm 2 knows its cost function and ±rm 1°s, but A/P Luo Xiao EC3312 - Lecture 8 23 March 2018 3 / 16
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Cournot Competition under Asymmetric Information Two ±rms choose their quantities q 1 and q 2 (of a homogeneous product) simultaneously. The market-clearing price is given by the inverse demand function P ( Q ) = a ° Q , where Q = q 1 + q 2 Firm 1°s cost function is: C 1 ( q 1 ) = cq 1 , where c < a . Firm 2°s cost function is: C 2 ( q 2 ) = ° c H q 2 , with probability θ c L q 2 , with probability 1 ° θ , where c L < c H < a Information is asymmetric: ±rm 2 knows its cost function and ±rm 1°s, but ±rm 1 knows its cost function and only that ±rm 2°s marginal cost is c H
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