Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). 1. Determine the range of values for x such that Player 2 has a strictly dominant strategy.
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Question 1
Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x).
1. Determine the range of values for x such that Player 2 has a strictly dominant strategy.
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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. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. 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? 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.Question 1 Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). A) Suppose that the value of x is such that player 2 has a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game? B) Suppose that the value of x is such the player 2 does NOT have a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game?Eva and Ethan love attending sports events, especially when they go together. However, Eva prefers watching field hockey while Ethan would rather go to a cricket match. If they go together, the payoff is higher for the person who favors the sports event more (payoff = 3), and less for the other person (payoff = 2). If they attend the events alone, the payoff is smaller and the same for each (payoff = 1). Show the payoff matrix for this couple and deter- mine the Nash equilibria. How do the payoffs from the Nash equilibria compare?
- 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. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.Brett and Oliver are both going surfing. Each can choose between "North Beach" (N) and "South Beach" (S). North beach is better, but they both also prefer having the beach to themselves rather than sharing it with the other person. If Brett chooses N and Oliver N, the payoffs are (60, 60). If Brett chooses N and Oliver Chooses S, the payoffs are (70,30). If Brett chooses S and Oliver N the payoffs are (30,70). If they both choose S the payoffs are (20,20). Brett gets to choose first and tells Oliver, who then makes a decision. Which of the following is true? O The number of nash equillibrium in this game is less than the number of subgame perfect equillibrium O The number of nash equillibrium in this game is the same as the number of subgame perfect equillibrium O The number of nash equillibrium in this game is more than the number of subgame perfect equillibrium O There is no subgame perfect equilibrium in this gameConsider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1 (if necessary). At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. In equilibrium, the payoff of Player 1 is ✓ and the payoff of player 2 is Player 2 L₂ (-1,8) L₁ Player 1 R₂ (100,1) R₁ (1,0)
- 4. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.UNIT 9 CHAPTER 5 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. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. 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? 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.Person A can trust or not trust person B. If person A decides to not trust, both players get a zero payoff. If Person A trusts, Person B can abuse or honour the trust bestowed upon them. If person B abuses Person A's trust, Person A gets a negative payoff. If person B honours person A's trust, person A gets a positive payoff. Person B can be of two types: trustworthy or not trustworthy. Both trustworthy and untrustworthy person B types get a positive payoff if they honour A's trust. But a trustworthy person B prefers to honour person A's trust whereas an untrustworthy B prefers to abuse. 2 Nature determines randomly if person B is trustworthy or not. Person B knows if they are trustworthy or not but person A doesn't know. The probability that person B is not trustworthy is a and the probability that person B is trustworthy is 1 a. a is common knowledge, meaning that both person A and person B know the probability of person B being (not) trustworthy. a) Draw the extensive game version…
- Alice chooses action a or action b, and her choice is observed by Bob. If Alice chooses action a, then Alice receives a payoff of 5 and Bob receives a payoff of 7. If Alice chooses action b, then Bob chooses action cor action d. If Bob chooses action c, then Alice receives a payoff of 10 and Bob receives a payoff of 5. If Bob chooses action d, then Alice receives a payoff of 0 and Bob receives a payoff of 3. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) O This game has imperfect information. O Alice's backward induction payoff is 5. O This is a promise game. O Alice's backward induction payoff is 0. O This is a prisoners' dilemma. O Bob's backward induction payoff is 5. O Bob's backward induction payoff is 3. O This is a threat game.CLASSES OF GAMES First, Alice chooses either action al or action a2. If Alice chooses action al, then she receives a payoff of 2 and Bob receives a payoff of 8. If Alice chooses action a2, then Bob chooses either action b1 or action b2. If Bob chooses action b1, then Alice receives a payoff of 0 and Bob receives a payoff of 2. If Bob chooses action b2, then Alice receives a payoff of 4 and Bob receives a payoff of 4. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) This game has perfect information. The strategy profile (a2,b1) is a Nash equilibrium of this game. Bob's backward induction payoff is 8. The strategy profile (al,b1) is a Nash equilibrium of this game. The strategy profile (a1,b2) is a Nash equilibrium of this game. The strategy profile (a2,b2) is a Nash equilibrium of this game. This is a bargaining game. This is a promise game. This is a threat game. Alice's backward induction payoff is 2.GAME ZZZ B1 Player B A1 30, 30 Player A A2 20, 40 B2 40, 20 35, 35 In the Game ZZZ (see table above), all payoffs are listed with the row player's payoffs first and the column player's payoffs second. In this game, neither player has a dominant strategy. the Nash equilibrium does not maximize the total payoff. there is no Nash equilibrium. the Nash equilibrium maximizes the total payoff.