Two players are playing a game in which each player requests an amount of money, simultaneously....
Two players are playing a game in which each player requests an
amount of money, simultaneously. The amount must be an integer
between 11 and 20, inclusive. Each player will receive the amount
she requests in $s. A player will receive an additional amount of
$20 if she asks an amount that is exactly 1 less than the other
player’s amount. All of the above is common knowledge.
a) Find the set of all pure-strategy Nash Equilibria.
b) Suppose we add one more rule to the game above: If the players
pick the same number, then they both get an additional $10. Find
the set of all pure-strategy Nash equilibria of this new game.
Homework Answers
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Two players are playing a game in which each player requests an
amount of money, simultaneously....
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
Suppose that two players are playing the following game
Suppose that two players are playing the following game. Player 1 can choose either top or bottom, and Player 2 can choose either left of right. The payoffs are given in the following table Player 2 Left Right top 9,4 2,3 Player 1 Bottom 1,0 3,1 where the number on the left is the payoff to Player 1 and the number on the right is the payoff to player 2. 1) Determine the nash equilibrium of the game. 2) If...
30 units. 5. Two players are playing a game. There are two options for player 1....
30 units. 5. Two players are playing a game. There are two options for player 1. Top or Bottom, and two options for player 2, Left or Right. The payoff matrix is as below. What is the pure Nash equilibrium in this case (Top, Left) b. (Top, Right) (Bottom, Top) a. c. d. (Bottom, Right) No pure Nash equilibrium. e. Left Right Top 5,5 0,4 Bottom 4,0 -1,-1
1. Find the Nash equilibria of the two-player strategic game in which each players set of...
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y,...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
NEED WITHIN THE HOUR! Suppose that two players are playing the following game. Player A can...
NEED WITHIN THE HOUR!
Suppose that two players are playing the following game. Player
A can choose either Top or Bottom, and Player B can choose either
Left or Right. The payoffs are given in the following table where
the number on the left is the payoff to Player A, and the number on
the right is the payoff to Player B.
Does Player A have a dominant strategy? If so, what is it?
Group of answer choices
Top is...
Consider the following version of the Rock-Paper-Scissors game. The two players have to choose simultaneously between...
Consider the following version of the Rock-Paper-Scissors game.
The two players have to choose simultaneously between
Rock(R), Paper(P) or Scissors(S).
According to this game, R beats S, S
beats P, P beats R. The winner gets 1
dollar from the other player. In case of a tie,the referee gives
both players 2 dollars. Payoffs for all possible choices are
summarized in the table below. Find all Nash Equilibria.
3) (25 points) Consider the following version of the Rock-Paper-Scissors game. The...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
30 units. 5. Two players are playing a game. There are two options for player 1. Top or Bottom, and two options for player 2, Left or Right. The payoff matrix is as below. What is the pure Nash equilibrium in this case (Top, Left) b. (Top, Right) (Bottom, Top) a. c. d. (Bottom, Right) No pure Nash equilibrium. e. Left Right Top 5,5 0,4 Bottom 4,0 -1,-1
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
NEED WITHIN THE HOUR!
Suppose that two players are playing the following game. Player
A can choose either Top or Bottom, and Player B can choose either
Left or Right. The payoffs are given in the following table where
the number on the left is the payoff to Player A, and the number on
the right is the payoff to Player B.
Does Player A have a dominant strategy? If so, what is it?
Group of answer choices
Top is...
Consider the following version of the Rock-Paper-Scissors game.
The two players have to choose simultaneously between
Rock(R), Paper(P) or Scissors(S).
According to this game, R beats S, S
beats P, P beats R. The winner gets 1
dollar from the other player. In case of a tie,the referee gives
both players 2 dollars. Payoffs for all possible choices are
summarized in the table below. Find all Nash Equilibria.
3) (25 points) Consider the following version of the Rock-Paper-Scissors game. The...
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