Question

In: Statistics and Probability

Consider the game in normal form given in the followingtable. Player 1 is the “row” player...

Consider the game in normal form given in the followingtable. Player 1 is the “row” player with strategiesA,BandCandplayer 2 is the “column” player with strategiesL,CandR. The gameis given in the following table:

L C R
A 0,0 2,-2 -2,3
B -2,2 0,0 2,-1
C 3,1 -1,2

0,1

(a) Find whether there is a mixed strategy Nash equilibrium (M.S.N.E) where player 1 mixes between A and C and player 2 mixes between L,C and R with positive probability.

(b) Find whether there exists a mixed strategy Nash equilibrium where each player mixes between all her strategies with positive probability.

Solutions

Expert Solution


Related Solutions

Consider the following strategic-form simultaneous game. Player 1’s payoffs are listed first, in bold Player 2...
Consider the following strategic-form simultaneous game. Player 1’s payoffs are listed first, in bold Player 2 W X Y Z Player 1 A 2 , 500 30 , 400 200 , 200 4 , 4 B 5 , 50 20 , 40   10 , 20 4 , 4 C 1 ,   0 1 ,   4 3 ,   2 4 , 4 Does either player have any weakly dominant strategies? If yes, list them. Briefly explain. Does either player have any...
Provide an example of a 2-player normal form game where each player has 3 (pure) strategies...
Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that: (i) There is exactly one pure strategy Nash equilibrium. (ii) There are exactly two pure strategy Nash equilibria. (iii) There are exactly three pure strategy Nash equilibria. (iv) There are exactly nine pure strategy Nash equilibria
1.       [Normal Form Game] Consider the following game on advertising and price strategy between two local...
1.       [Normal Form Game] Consider the following game on advertising and price strategy between two local businesses (P is price and A is advertising). Payoffs are representative of profits. Find the Nash equilibrium. If there was collusion between the two businesses, could they cooperate and improve their profits? Sarah’s Sandwiches Bandit’s Bagels Low P, Low A Low P, High A High P, Low A High P, High A Low P, Low A 30, 20 20, 25 35, 15 30, 30...
Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is...
Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is a debtor country. Reform Waste Aid 3, 2 -2, 3 No Aid -2, 1 0, 0 a) Compute all (pure and mixed) Nash equilibria. b) Do you think that the above game is the case of a resource curse? Interpret the game with a story of a resource curse.
11. Given a row echelon form or the reduced row echelon form of an augmented matrix...
11. Given a row echelon form or the reduced row echelon form of an augmented matrix of a system of equations, determine the number of solutions the system has.
Consider the following game. Player 1’s payoffs are listed first:                        Player 2 X Y Player...
Consider the following game. Player 1’s payoffs are listed first:                        Player 2 X Y Player 1 A 90 , 1 10 , 0 B 10 , 0 50 , 1 C 100 , 0 80 , 1 Imagine that player 1 makes a decision first and Player 2 makes a decision after observing player 1’s choice. What is the subgame-perfect equilibrium of this game? Imagine that player 2 makes a decision first and Player 1 makes a decision after...
1. Consider the following normal form game: 1\2 X Y Z A 3,3 0,5 0,4 B...
1. Consider the following normal form game: 1\2 X Y Z A 3,3 0,5 0,4 B 0,0 3,1 1,2 C -1,5 2,2 0,1 a. Does the game have a dominant strategy solution? If yes, which one? (no proof needed) (10 pts)                                                                                                          b. Does the game have a solution to IEDS? What is it? Show your procedure. (10 pts)
Consider a game in which, simultaneously, player 1 selects any real number x and player 2...
Consider a game in which, simultaneously, player 1 selects any real number x and player 2 selects any real number y. The payoffs are given by: u1 (x, y) = 2x − x2 + 2xy u2 (x, y) = 10y − 2xy − y2. (a) Calculate and graph each player’s best-response function as a function of the opposing player’s pure strategy. (b) Find and report the Nash equilibria of the game. (c) Determine the rationalizable strategy profiles for this game.
Consider a game between a tax collector (player 1) and a tax payer (player 2).  Player2 has...
Consider a game between a tax collector (player 1) and a tax payer (player 2).  Player2 has an income of 200 and may either report his income truthfully or lie.  If he reports truthfully, he pays 100 to player 1 and keeps the rest.  If player 2 lies and player 1 does not audit, then player 2 keeps all his income.  If player 2 lies and player 1 audits then player 2 gives all his income to player 1. The cost to player 1...
Question 1. Put the following game into the normal form. That is, describe the set of...
Question 1. Put the following game into the normal form. That is, describe the set of players, the strategy sets for each player, the payoff functions, and draw the game in matrix form. What do you expect would happen in this game, and why?Two kids are playing a game of Chicken. In this game, they ride their bikes as fast as theycan at each other. The one to swerve or turn out of the way loses, he is a Chicken...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT