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GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
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...
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...
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...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
Consider a game being played between player 1 and player 2. Player 1 can choose T...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
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...
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
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4 DOWN 2,3 3,2 a. If there is a Nash equilibrium in pure strategies, what is it and what are the payoffs? b. If there is a Nash equilibrium in mixed strategies, what is it and what are the expected payoffs? 3. Continue with the previous game but suppose this was a sequential game where Player A got to go first. a. Diagram the game...
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).
Consider the following non-cooperative, 2-player game. Each player is a manager who wishes to get a...
Consider the following non-cooperative, 2-player game. Each
player is a manager who wishes to get a promotion. To get the
promotion, each player has two possible strategies: earn it through
hard work (Work) or make the other person look bad through
unscrupulous means (Nasty). The payoff matrix describing this game
is shown below. The payoffs for each player are levels of
utility—larger numbers are preferred to smaller numbers. Player 1’s
payoffs are listed first in each box.Find the Nash
equilibrium...
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...
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...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
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).
Consider the following non-cooperative, 2-player game. Each
player is a manager who wishes to get a promotion. To get the
promotion, each player has two possible strategies: earn it through
hard work (Work) or make the other person look bad through
unscrupulous means (Nasty). The payoff matrix describing this game
is shown below. The payoffs for each player are levels of
utility—larger numbers are preferred to smaller numbers. Player 1’s
payoffs are listed first in each box.Find the Nash
equilibrium...
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