Left Right Up 1, 3 3, 1 Down 2, 2 4, 4 a. Find the Nash equilibrium or equilibria b. Which player, if any, has a dominant strategy? c. Does A benefit from changing the game by reducing his or her payoff in this way?
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- 4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.6. Consider Jake and Al again. They are considering going to Portugal or Sweden once the pandemic ends. Here are their payoffs: Al's choices: Sweden Portugal Jake's choices (8, 4) (4, 9) Sweden (10, 5) Portugal (3, 6) and Al going to d) The strategy (P, S), represents Jake going to e) Is there a dominant strategy in this game? Explain. f) Find the Nash equilibrium (equilibria) in this game, if one or more exists.1. Assume this game is played 2 times and there is no discounting. The whole payoff for two periods is the sum of payoffs of each period. Draw a tree of the game and solve it with subgame prefect Nash equilibrium. Explain clearly, handwritten is preferable.
- 2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 53. Write a normal form representation of the game shown in the figure below and derive all pure strategy Nash equilibria. P1 L R P2 P2 L R R l's Payoff 1 2's Payoff 25. Consider the following Extended Form game where P1 stands for Player one and P2 stands for player two with A, B and A', B' being their respective strategies. A' (1,1) P2 B' (2,3) P1 A' B (4,5) P2 What is the set of Nash Equilibria? Clearly explain your answer. Full-screen Snip B' (6,7)
- 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 clearlyi. 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.Which is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)
- Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?3. How many extensive forms are there that are equivalent to the following normal form game (pay attention to the payoffs in the matrix)? You may rename strategies, if necessary. Show the extensive forms. II ti t2 t3 t4 ts to si 7,1 2,2 | 1,5 7,1 I 2,2 1,5 S2 3,3 3,3 | 3,3 2,1 2,1 2,1