b. You and your friend are gambling and each of you have two balls: yellow and blue. If the colour of the ball picked by you is the same as your friend's, you win. If the colour of the balls draw from you and your friend are different, your friend wins. Winning with a yellow ball earns a payoff of $100, while winning with a blue ball earns a payoff of $80. i. What is(are) the Nash equilibrium (equilibria), if any, under pure strategies in the above simultaneous game? i. What is the Nash equilibrium under mixed strategy? iii. What is the expected payoff for you and your friend under the mixed strategy in (ii.)?
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- . In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? c. Determine the optimal strategies and the value of this game. Does the game favor one player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 ہے A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy. с.
- Game 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…Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearlyPlease help awnser 7. Game TheoryAlice and Bob playing the following 2x3 game. In the payoff matrix below, Alice’s payoffsare the first number and Bob’s are the second number.
- 3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 8The next 3 questions involve the following game. There are two players, a husband and wife. They can either be selfish (S) or selfless (U) in their marriage. If they choose to be selfish, then there is a negative ʻguilt’ payoff of g. The payoff matrix is below. Figure 1: The Marriage Game Wife S U S 10-g, 10-g 15-g, 2 U 2, 15-g 12, 12 Number left (right) of comma refers to H's (W's) payoff. 23. Suppose that g = 0. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 24. Suppose that g= 5. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 25. Suppose that g = 10. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). HusbandThe bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA O O 2 Calculate Rowena 's expected payoff in the mixed strategy Nash equilibrium. 3.5 2.5 Up Down 3 Left 1,16 2,20 COLIN Right 4,6 3,40
- learn.canterbury.ac.nz Clasarsom Nov 15-ICO EUC LEARN | AKO See the game below and answer the questions 8 to 11: Player-1 C Player-2 X, Y Y Player-1 9 14 8. Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X O b. Playert: C; Player2: Y Oc. Playert: L; Player2: X Od. Playert: L; Player2: Y e. None2. Consider the following game. Two criminals are thinking about pulling off a bank robbery. The take from the bank would be $20,000 each, but the job requires two people (one to rob the bank and one to drive the getaway car. Each criminal could instead rob a liquor store. The take from robing a liquor store is only $1000 but can be done with one person acting alone. Write the payoff matrix of this game Player A Bank job Liqour store Player B Bank job Liquor store a. What are the Nash equilibria in this game? b. Explain why there can be multiple equilibria in this game. c. How the game will be played if mixed strategies are allowed? Discuss.Question 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.