Consider the following 2-player normal form game. Player 2 Bananas Orange Player 1 Grapes 11, 3 8, 2 Apple 9, 7 6, 5 Player 1's dominant strategy is [Select ] and Player 2's dominant strategy is ( Select ) The Nash Equilibrium of this game is ( Select ) (select all that apply).
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- Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry's payoff is the fiırst number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [ Select ] v and Kerry will [ [ Select ]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 ofconside the following game There are two companies that sell Haitian coffee.Each company currently makes $5 million in revenue They need to determine whether they should engage in a social media advertising campaign Advertising costs $2 million for each company If one company advertises and the other does not, then the one that advertises captures $3 million from the company that does not. If both companies advertise they gain nothing. Draw the payoff matrix. What is this games Nash equilibrium
- Consider the following representation of a hockey shootout. The shooter can shoot on their forehand, or deke to their backhand, and the goalie can anticipate either move. The number in each cell in the table below represents the percentage chance that the shooter scores for each pair of pure strategies. Anticipate Forehand Anticipate Backhand Shoot Forehand 20 40 Deke Backhand 40 10 In the mixed strategy Nash equilibrium of this game, what is the percentage chance that the player scores? (ie. An 80% chance should be recorded as 80)Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 50, 50 -110, 6 B 6, -110 26, 26 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.check all that apply (26,26) (50,50) (-110,6) (6,-110) Which of these outcomes would you consider most likely?multiple choice 1 (-110,6) (50,50) (6,-110) (26,26) b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?multiple choice 2 B A What outcome do you think would occur as a result?multiple choice 3 (26,26) (50,50) (-110,6) (6,-110) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move…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.
- Find all of the Nash equilibrium of the following three player game. Player 1 chooses rows (a,b). Player 2 chooses columns (c,d). Player 3 chooses matrices (x.y). Player 3 receives the third listed payoff for cach outcome. 5,5,5 4,4,0 8,8,3 7,7,3 1,3,1 4,2,0 3,2,4 3,1,0 a by A) (b,d.x) and (a,d.y) B) (b.cy) OC) (b,d,x) D) (a,d,x) and (b,c.y) E) (b,c,x) OF) (a,d.x)The world has changed a bit. Microsoft and Google could still either cooperate or compete in the market for social media video software currently captured by Tik Tok, but their payoffs have changed. The table below shows their profits in billions of USD in each scenario. Use your mouse to point and click on the Nash equilibrium outcome(s). [There may be more than one so make sure you work out all the best response strategies]. Microsoft Cooperate 3,3 4,0 Cooperate O Don't cooperate O Google Don't cooperate O O 0,4 1,1Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
- Team 2 plays A Team 2 plays B Team 2 plays C Team 1 plays A 9, 9 8, 12 6, 6 Team 1 plays B 6, 6 0, 7 5, 5 Team 1 plays C 12, 8 10, 10 7,0 Consider the simultaneous move game above in which two teams are competing against each other. Which of the following statements are true? In all Nash Equilibria of the game Team 2 plays B This game has two Nash Equilibria Team 1's best response to team 2 playing B is to play A. O None of the other answers are correct This game has a mixed strategy Nash Equilibria where a player randomizes over multiple options.Team 2 plays A Team 2 plays B Team 1 plays A 2, 1 0,0 Team 1 plays B 0,0 1, 2 Consider the game above. Which of the following is a Nash Equilibrium of the game? O Team 1 plays A two thirds of the time and plays the rest of the time, while team 2 plays A two thirds of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A one quarter of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A three quarters of the time and plays B the rest of the time. O None of the other answers are correct. Team 1 plays A two thirds of the time and plays B the rest of the time, while team 2 plays A one third of the time and plays B the rest of the time.Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1. 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. For player 2, A stands for Accommodate and F stands for Fight. Player 1 Enter Player 2 A F A Stay out Player 2 F (16,30) (-6,18) In the Nash equilibrium of this game, player 2 earns Player 2 player 1 would play (0,40) (0,20) ✓an incentive to threaten F because, if player 1 believed him then so that player 2 would earn ✓. However, this threat is