d. Find the mixed strategy Nash Equilibrium (msNE) of the game. [Hint: denote by p the to Swerve. Similarly let q be the probability that Player 2 chooses Straight and (1-q) the probability that she chooses to Swerve.] e. Draw a figure with probability p in the horizontal axis and probability q in the vertical axis to depict each player's best response function. Make sure to identify the psNEs you found in part (c) and the msNE you found in part (d). f. Consider now that the game is sequential, with Player 1 choosing between Straight or Swerve as the leader and Player 2, observing Player 1's choice, responds with Straight or Swerve. Find the Subgame Perfect Nash Equilibrium (SPNE) of the game. Interpret why the SPNE of the game differs from the msNE you found in part (d)
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Nsider the Game of Chicken depicted in the figure below, in which t each other must decide whethe...
4) (20 points) Consider the following two player simultaneous move game which is another version of...
4) (20 points) Consider the following two player simultaneous move game which is another version of the Battle of the Sexes game. Bob Opera Alice 4,1 Opera Football Football 0,0 1,4 0,0 Suppose Alice plays a p - mix in which she plays Opera with probability p and Football with probability (1 – p) and Bob plays a q- mix in which he plays Opera with probability q and Football with probability (1 – 9). a) Find the mixed strategy...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
1. In the game below A chooses rows and B (i) Find all the strategies that...
1. In the game below A chooses rows and B
(i) Find all the strategies that survive iterated deletion of
strictly dominated strategies (IDSDS)
(ii) Find each player’s best responses and the Nash
Equilibrium
2. Consider the game structure below for the next several
questions:
(i) What must be true about the values of a, b, c, and d in
order for U to be a strictly dominated strategy?
(ii) What must be true about the values of a, b,...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. Assume that past actions are commo...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75....
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75. 2 6, 31, 10 Let p be the probability that player 2 plays R and let q be the probability that player 1 plays T. Draw a pair of axes with p on the horizontal axis and q on the vertical axis. Draw two lines, one indicating player 1's best response(s) as a function of p and another indicating player 2's best response(s) as...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of...
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...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
s Use the following one-shot, normal-form game to answer the questions below Player 2 Strategy Player...
s Use the following one-shot, normal-form game to answer the questions below Player 2 Strategy Player 1 A 100, 100 150,200 200 200, 75 300, 200 125, 150 100, 225 200, 300 225, 195 150, 250 c Find each player's dominant strategy, if it exists.(4 points) d. Find each player's secure (maximin) strategy. (4 points) Find the Nash equilibrium, if there is one, and explain why it is the Nash equilibrium. If there is not a Nash equilibrium, explain why....
4) (20 points) Consider the following two player simultaneous move game which is another version of the Battle of the Sexes game. Bob Opera Alice 4,1 Opera Football Football 0,0 1,4 0,0 Suppose Alice plays a p - mix in which she plays Opera with probability p and Football with probability (1 – p) and Bob plays a q- mix in which he plays Opera with probability q and Football with probability (1 – 9). a) Find the mixed strategy...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
1. In the game below A chooses rows and B
(i) Find all the strategies that survive iterated deletion of
strictly dominated strategies (IDSDS)
(ii) Find each player’s best responses and the Nash
Equilibrium
2. Consider the game structure below for the next several
questions:
(i) What must be true about the values of a, b, c, and d in
order for U to be a strictly dominated strategy?
(ii) What must be true about the values of a, b,...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75. 2 6, 31, 10 Let p be the probability that player 2 plays R and let q be the probability that player 1 plays T. Draw a pair of axes with p on the horizontal axis and q on the vertical axis. Draw two lines, one indicating player 1's best response(s) as a function of p and another indicating player 2's best response(s) as...
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...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
s Use the following one-shot, normal-form game to answer the questions below Player 2 Strategy Player 1 A 100, 100 150,200 200 200, 75 300, 200 125, 150 100, 225 200, 300 225, 195 150, 250 c Find each player's dominant strategy, if it exists.(4 points) d. Find each player's secure (maximin) strategy. (4 points) Find the Nash equilibrium, if there is one, and explain why it is the Nash equilibrium. If there is not a Nash equilibrium, explain why....
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