QUESTION 7 Player 2 Left Right P1: $6 P1:$0 Player 1 Up P2: $6 P2: $5 P1: $3 P1: $1 Down P2:$8 P2: $10 List all dominant stragies in the game shown above O Up is a dominant strategy for player 1 O Down is a dominant strategy for player 1 O Left is a dominant strategy for player 2 Right is a dominant strategy for player 2 O There are no dominant strategies in this game
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![QUESTION 7
Player 2
Left
Right
P1: $6
P1:$0
Player 1
Up
P2: $6
P2: $5
P1: $3
P1: $1
Down
P2:58
P2: $10
List all dominant stragies in the game shown above
O Up is a dominant strategy for player 1
O Down is a dominant strategy for player 1
O Left is a dominant strategy for player 2
O Right is a dominant strategy for player 2
O There are no dominant strategies in this game](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b01e03f-a2d2-46d7-a6ad-1af362e2fbb8%2F05be612b-6868-415a-9b12-3d800a8d3fe1%2Fmk56cih_processed.jpeg&w=3840&q=75)
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- Player 1 ооооо Up Down List all dominant strategies in the game shown above Up is a dominant strategy for player 1 Down is a dominant strategy for player 1 Left is a dominant strategy for player 2 Right is a dominant strategy for player 2 There are no dominant strategies in this game Player 2 Left P1: $15 P2: $15 P1: $12 P2: $18 Right P1:$11 P2: $16 P1: $13 P2: $13Player 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. Does either player have a dominant strategy? Player one has a dominant strategy. Player two has a dominant strategy. Both players have a dominant strategy. Neither player has a dominant strategy.Player 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. What is the Nash equilibrium in this game? Strategy 1 and Strategy A Strategy 2 and Strategy A Strategy 2 and Strategy B This game does not have a Nash equilibrium
- Up ооооо Down Player 1 Up No EFFICIENT equilibrium exists Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) P1 gets $15 P2 gets $25QUESTION 9 D 2 C D D, D OD, C C, D C II C (2,2) (4,0) (0,4) (3,3) In the dynamic game represented by the graph above, the numbers inside paranthesis show the payoffs of Player 1 and Player 2, respectively. The Nash equilibrium of this game is for Player 1 to choose O C, C and Player 2 to choose5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.
- The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofi. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.3. Player 1 and Player 2 are going to play the following stage game twice: Player 1 Top Bottom Left 4,3 0,0 Player 2 Middle 0,0 2,1 Right 1,4 0,0 There is no discounting in this problem and so a player's payoff in this repeated game is the sum of her payoffs in the two plays of the stage game. (a) Find the Nash equilibria of the stage game. Is (Top, Left) a Nash of the stage game? (b) Find a subgame perfect Nash equilibrium of the repeated game where the first time they play the stage game Player 1 chooses Top and Player 2 chooses Left.
- 5) Mixed strategy Nash equilibrium Consider a mixed strategy Nash equilibrium of the following coordination game: Player 2 Player 1 A B a 5.5 6.-2 b -2,6 1,1 a) In the above game, explain in words what condition player 1's probability p of playing strategy A must satisfy to induce player 2 to mix strategies between a and b in equilibrium. b) Solve for the mixed strategy Nash equilibrium where player 1 chooses A with probability P and player 2 chooses a with probability p, for 0 < p, P < 1.A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?7 In bargaining theory, sometimes an individual’s patience level can affect his or her bargaining power. Consider a simple repeated game in which Person 1 makes an offer to purchase a good that Person 2 is selling; Person 2 can either accept this offer or reject it and make a counteroffer. This game continues until one player accepts the other’s offer. Explain how incorporating the rate of time preference (ββ) into such a repeated game might alter the outcome.