Homework Answers
A dominant strategy of a player is the strategy that always makes the player better off, no matter what his opponent chooses.
In the given game, when player 2 plays X, it is best for player 1 to choose B because payoff 5 from choosing B is greater than payoff 3 from choosing A. And if, player 2 plays Y, then it will be the best for player 1 to choose B, because 1 from choosing B is greater than 0 from choosing A.
So it can be seen that, no matter what player 2 plays, player 1 is always better off by choosing B. So 'B' is player 1's dominant strategy.
Now for player 2, when player 1 plays A, player 2 will be better off by choosing Y (because 5>3) and when player 1 plays B, player 2 again will be better off by playing Y (because 1 > 0). So, 'Y' is Player 2's dominant strategy.
Therefore, the Nash equilibrium is (B,Y) : (1,1).
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find any dominant strategies and any nash equilibrium
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find any dominant strategies and any nash equilibrium Player 2 X Y 10,10 15,5 Player 5,...
find any dominant strategies and any nash equilibrium
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Game Theory Nash Equilibrium Mixed strategies for 2*3 Matrix
a) Eliminate strictly dominated strategies.b) If the game does not have a pure strategy Nash equilibrium,find the mixed strategy Nash equilibrium for the smaller game(after eliminating dominated strategies). Player 2Player 1abcA4,33,22,4B1,35,33,3
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Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A...
Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A 4,0 -3,8 -7, -1 B-4,3 0,6 9,5 C3,2 2,-1 11, 9 Let B1(-) and B2(-) be the best response function for player 1 and player 2 respectively. Calculate the following: 3)a) [1pt] B1(X) 3)b) [1pt] B2(B) 3)c) (1pt] Social Welfare Maximum: 3)d) [1pt] Dominant Strategies for Player 1: 3)) [1pt] Pure Nash Equilibriums:
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and...
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The following matrix gives the payoff for Player 1 and Player 2 with R and L...
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5. Explain the difference between a Nash equilibrium and a dominant strategies equilibrium. Give an example...
5. Explain the difference between a Nash equilibrium and a dominant strategies equilibrium. Give an example to show how the prisoners' dilemma helps to explain behaviour. 6. Why might a firm set prices based on a markup above average cost rather than equalising marginal costs and marginal benefits? 7. Using a diagram, explain how an external cost of production (i.e. a negative production externality) can be internalised with a tax. |8. Explain the conditions of price discrimination. Give two examples...
Exercise 4: For the game "Rock-Paper-Scissors". a. Prove that there is no Nash Equilibrium in pure strategies b. Explai...
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find any dominant strategies and any nash equilibrium
Player 2 X Y 10,10 15,5 Player 5, 15 12, 12
Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A 4,0 -3,8 -7, -1 B-4,3 0,6 9,5 C3,2 2,-1 11, 9 Let B1(-) and B2(-) be the best response function for player 1 and player 2 respectively. Calculate the following: 3)a) [1pt] B1(X) 3)b) [1pt] B2(B) 3)c) (1pt] Social Welfare Maximum: 3)d) [1pt] Dominant Strategies for Player 1: 3)) [1pt] Pure Nash Equilibriums:
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of matching pennies as described above. If the pennies match player 2 pays player 1 $1 (both get head or tail). If the pennies are not matched player 1 pays player 2 $1 ( head , tail or tail , head). H represents heads and T represents Tails 1. (2 points) What is the set of strategies for each player? 2. (5 points) Is there...
5. Explain the difference between a Nash equilibrium and a dominant strategies equilibrium. Give an example to show how the prisoners' dilemma helps to explain behaviour. 6. Why might a firm set prices based on a markup above average cost rather than equalising marginal costs and marginal benefits? 7. Using a diagram, explain how an external cost of production (i.e. a negative production externality) can be internalised with a tax. |8. Explain the conditions of price discrimination. Give two examples...
Exercise 4: For the game "Rock-Paper-Scissors". a. Prove that there is no Nash Equilibrium in pure strategies b. Explain why the only Nash Equilibrium in mixed strategies where, in stead of choosing a given strategy, a player can randomize between any number of its available strategies) is to show Rock, Scissors or Paper with probability 1/3 each.
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