class 20 dynamic games post2

class 20 dynamic games post2 - Class 20 Bertrand...

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Class 20 ertrand Competition Bertrand Competition Dynamic Games
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Problem Set ote the Reading ± Note the Reading ± Do the problem set before the next lecture: You train today’s material and prepare for next time
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Last Time: Nash Equilibrium ash Equilibrium Left Right Left 1 / 1 - 10 / - 10 Nash Equilibrium An action profile ( a* 1 , a* 2 ) is a Nash Equilibrium if: Right - 10 / - 10 1 / 1 u 1 (a* 1 , a* 2 ) u 1 (a’ 1 , a* 2 ) for all a’ 1 u 2 (a* 1 , a* 2 ) u 2 (a* 1 , a’ 2 ) for all a’ 2 Interpretation I: Stable Convention ash quilibrium Interpretation II: Consistent Prediction Nash Equilibrium: Idea: Players know the ctions f ach ther nd A Nash equilibrium is a stable convention for a society/group of player: No member has an incentive eviate A prediction about which actions are played should be a Nash Equilibrium. Otherwise, players who know the actions of each other and each player plays a best response. to deviate. prediction would not play according to it. Iterated Elimination: Players know preferences and common knowledge of rationality.
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Outline ertrand Competition ± Bertrand Competition ± Dynamic Games: ± Nash Equilibrium ± Subgame-Perfection and Backward Induction ± Stackelberg
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Price Competition: Amazon
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Price Competition: Amazon ertrand Game ertrand Game: Equilibrium Bertrand Game Two sellers offer a book to a buyer Buyer’s valuation v , Sellers’ costs c = 0 Bertrand Game: Equilibrium Prices must be zero in all equilibria: Could there be an equilibrium with Buyer buys from the cheaper seller Actions: p in [c,v] p 2 > 0 ? What would p 1 be?
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This note was uploaded on 12/10/2011 for the course ECON 401 taught by Professor Burbidge,john during the Winter '08 term at Waterloo.

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class 20 dynamic games post2 - Class 20 Bertrand...

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