Player 2 Left P1: $40 Player 1 Up P2: SO P1: $44 Down P2:$44 In the game shown above, list all of the EFFICIENT Nash Equilibrium (please check ALL that apply) (up, left) (up, right) (down, left) (down, right) No efficient Nash Equilibrium Right P1:$1 P2: $1 P1: $0 P2: $40
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- Player 1 оооо Up (up, left) (up, right) (down, left) (down, right) None Down Player 2 Left P1: $15 P2: $15 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) P1: $12 P2: $18 Right P1:$11 P2: $16 P1: $13 P2: $13Player 2 Middle Left P1: $45 P1: $70 Up P2: $45 P2: $50 Player 1 P1: $50 P1: $60 Middle P2: $50 P2: $60 P1: $60 P1: $50 Down P2: $60 P2: $70 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, left) (up, middle) (up, right) (middle, left) (middle, middle) (middle, right) (down, left) (down, middle) (down, right) No equilibrium Right P1: $45 P2: $60 P1: $50 P2: $70 P1: $60 P2: $60Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…
- Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff ofROWENA 2 Answer 1: 2 Answer 2: 2 Answer 3: 1 Earth Water Wind Answer 4: Fire of the Nash equilibrium, (Rowena's 1 Colin's 3 3 North 1.3 This simultaneous game has two Nash equilibria. The Nash equilibrium, (Rowena's 2 , Colin's 1,2 3,2 2,0 COLIN South 3,1 1,2 2,1 3,0 East 0,2 2,3 1,1 West 1.1 1,1 0,3 2,2 ) has a greater joint payoff than that
- Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays upQ3 Consider the following three-player normal form game (Player 3 is the page player): Player 3 A в Player 2 Player 2 A в A B 1,2, 3 в 2,3,1 Player 1 A Player 1 A 2, 1, 3 3, 2, 1 3, 2, 1 1,2, 3 в 1,3, 2 3, 1,2 For each player, strategies are A and B. a) Find the pure strategy Nash equilibrium of the above game. Assume now that the above game is played sequentially, with Player 3 moving first, Player 1 moving second, and Player 2 moving third. b) Write down the game tree. c) For each player, list all the available pure strategies. d) Find the subgame perfect equilibrium outcome and compare it with the equilibrium outcome you found in subquestion a). Comment.Lee and Cody are playing a game in which Lee has the first move at A in the accompanying decision tree: Once Lee has chosen either aggression or cooperation, Cody, who can see what Lee has chosen, must choose either aggression or cooperation at B or C. Both players know the payoffs at the end of each branch. Lee chooses A Aggression Cooperation Cody chooses 8 Multiple Choice C Cody chooses Aggression aggression: aggression Cooperation Aggression In the equilibrium of this game, Lee chooses Cooperation aggression; cooperation -10 for Lee -10 for Cody 40 for Lee O for Cody O for Leo 40 for Cody 25 for Lee 25 for Cody and then Cody chooses.
- i. 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.This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). B Right (2, 2) (1, 3) Left (3, 1) (0,0) Up A Down Which outcome is the Nash equilibrium in this game? (Up, Right) (Up, Left) (Down, Right) (Down, Left)Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.