201Winter2010PartIV

201Winter2010PartIV - Class 14: Reaction Functions...

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Class 14: Reaction Functions . A Reaction Function y 1 = F ( y 2 ) depicts the best-response y 1 of Player 1 to all possible actions y 2 by the Player 2. FIGURE 14.1 HERE FIGURE 14.2 HERE Remark . Reaction functions are derived from optimization behavior. 1
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Class 15: Nash Equilibrium with Continuous Choice simultaneous-move games with two players. Let y 1 denote the action of player 1 and y 2 denote the action of player 2. Let y 1 = F ( y 2 ) denote the reaction function of player 1 and let y 2 = G ( y 1 ) denote the reaction function of player 2. In a Nash Equilibrium the equilibrium strategies ( y 1 ;y 2 ) satisfy conditions y 1 = F ( y 2 ) and y 2 = F ( y 1 ) : Remark In the N.E. both ". Example: Oligopoly with Quantity-Competition with Simultaneous Moves q 1 : q 2 : that supply equals demand. Assume that the demand curve is D ( p ) = 1000 p; where p denotes price : 2
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The inverse demand curve is therefore p = 1000 q: The inverse demand curve is derived q = 1000 p " and then solving this equation for p: q = q 1 + q 2 . unit of output) is c C ( q 1 ) = cq 1 C ( q 2 ) = cq 2 Our objective as economists ( q 1 ;q 2 ) in equilibrium and for the equilibrium price p : SOLUTION STRATEGY: STEP 1. Solve for the reaction function q 1 ( q 2 )
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This note was uploaded on 04/07/2010 for the course ECONOMIC 201 taught by Professor Mikko during the Winter '10 term at Waterloo.

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201Winter2010PartIV - Class 14: Reaction Functions...

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