ECE1010-09

# ECE1010-09 - UNIT III COMPETITIVE STRATEGY Monopoly...

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UNIT III: COMPETITIVE STRATEGY • Monopoly • Oligopoly • Strategic Behavior 12/3

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Strategic Competition Dominance Reasoning Best Response and Nash Equilibrium Mixed Strategies Repeated Games The Folk Theorem Cartel Enforcement
Dominance Definition Dominant Strategy : a strategy that is best no matter what the opponent(s) choose(s). T 1 T 2 T 3 T 1 T 2 T 3 0,2 4,3 3,3 4,0 5,4 5,6 3,5 3,5 2,3 0,2 4,3 3,3 4,0 5,4 5,3 3,5 3,5 2,3 S 1 S 2 S 3 S 1 S 2 S 3 Sure Thing Principle : If you have a dominant strategy, use it! (S 2 ,T 3 ) (S 2 ,T 2 )

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Nash Equilibrium Definitions Best Response Strategy : a strategy, s*, is a best response strategy, iff the payoff to (s*,t) is at least as great as the payoff to (s,t) for all s. -3 0 -10 -1 5 2 -2 -4 0 0,4 4 ,0 5,3 4 ,0 0,4 5,3 3,5 3,5 6 ,6 S 1 S 2 S 3 S 1 S 2 S 3 T 1 T 2 T 3 Nash Equilibrium : a set of best response strategies (one for each player), (s*, t*) such that s* is a best response to t* and t* is a b.r. to s*. (S 3 ,T 3 )
Nash Equilibrium -3 0 -10 -1 5 2 -2 -4 0 4,4 2 ,3 1,5 3,2 1,1 0,0 5 ,1 0,0 3 ,3 S 1 S 2 S 3 S 1 S 2 S 3 T 1 T 2 T 3 Nash equilibrium need not be Efficient.

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Nash Equilibrium -3 0 -10 -1 5 2 -2 -4 0 1 ,1 0,0 0,0 0,0 1 ,1 0,0 0,0 0,0 1 ,1 S 1 S 2 S 3 S 1 S 2 S 3 T 1 T 2 T 3 Nash equilibrium need not be unique. A COORDINATION PROBLEM
Nash Equilibrium -3 0 -10 -1 5 2 -2 -4 0 1 ,1 0,0 0,0 0,0 1 ,1 0,0 0,0 0,0 3 ,3 S 1 S 2 S 3 S 1 S 2 S 3 T 1 T 2 T 3 Multiple and Inefficient Nash Equilibria.

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Nash Equilibrium -3 0 -10 -1 5 2 -2 -4 0 1,1 0,0 0,-100 0,0 1,1 0,0 -100,0 0,0 3,3 S 1 S 2 S 3 S 1 S 2 S 3 T 1 T 2 T 3 Multiple and Inefficient Nash Equilibria. Is it always advisable to play a NE strategy? What do we need to know about the other player?
Button-Button Left Right L R L R (-2,2) (4,-4) (2,-2) (-1,1) Player 1 Player 2 Player 1 hides a button in his Left or Right hand. Player 2 observes Player 1’s choice and then picks either Left or Right. How should the game be played? GAME 2.

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Button-Button Left Right L R L R (-2,2) (4,-4) (2,-2) (-1,1) Player 1 Player 2 Player 1 should hide the button in his Right hand. Player 2 should picks Right. GAME 2.
Button-Button Left Right L R L R (-2,2) (4,-4) (2,-2) (-1,1) Player 1 Player 2 What happens if Player 2 cannot observe Player 1’s choice? GAME 2.

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Button-Button Left Right L R L R (-2,2) (4,-4) (2,-2) (-1,1) Player 1 Player 2 -2, 2 4 , -4 2 , -2 -1, 1 L R L R GAME 2.
Mixed Strategies -2, 2 4, -4 2, -2 -1, 1 Definition Mixed Strategy : A mixed strategy is a probability distribution over all strategies available to a player. Let (p, 1-p) = prob. Player 1 chooses L, R. (q, 1-q) = prob. Player 2 chooses L, R. L R L R GAME 2.

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Mixed Strategies -2, 2 4, -4 2, -2 -1, 1 Then the expected payoff to Player 1: EP 1 (L) = -2(q) + 4(1-q) = 4 – 6q EP 1 (R) = 2(q) – 1(1-q) = -1 + 3q Then if q < 5/9, Player 1’s best response is to always play L (p = 1) L R L R (p) (1-p) (q) (1-q) GAME 2.
q LEFT 1 5/9 RIGHT 0 0 1 p p*(q) Button-Button Player 1’s best response function. GAME 2.

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Mixed Strategies -2, 2 4, -4 2, -2 -1, 1 Then the expected payoff to Player 1: EP 1 (L) = -2(q) + 4(1-q) EP 1 (R) = 2(q) – 1(1-q) (Equalizers) q* = 5/9 and for Player 2: p* = 1/3 EP 2 (L) = 2(p) - 2(1-p) EP 2 (R) = -4(p) + 1(1-p) L R L R (p) (1-p) (q) (1-q) NE = {(1/3), (5/9)} GAME 2.
q LEFT 1 5/9 RIGHT 0 0 1/3 1 p q*(p) p*(q) NE = {(1/3), (5/9)} Button-Button GAME 2.

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2x2 Game T 1 T 2 1. Prisoner’s Dilemma 2. Button – Button 3. Stag Hunt 4. Chicken 5. Battle of Sexes S 1 S 2 x 1 ,x 2 w 1 , w 2 z 1 ,z 2 y 1 , y 2
Stag Hunt T 1 T 2 S 1 S 2 5 ,5 0,3 3,0 1 ,1 also Assurance Game NE = {(S 1 ,T 1 ), (S 2 ,T 2 )} GAME 3.

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Chicken T 1 T 2 S 1 S 2 3,3 1 ,5 5 ,1 0,0 also Hawk/Dove NE = {(S 1 ,T 2 ), (S 2 ,T 1 )} GAME 4.
Battle of the Sexes T 1 T 2 S 1 S 2 5 ,3 0,0 0,0 3 ,5 NE = {(S 1 ,T 1 ), (S 2 ,T 2 )} GAME 5.

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ECE1010-09 - UNIT III COMPETITIVE STRATEGY Monopoly...

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