(ZERO-SUM GAME) Consider the game X [1 al. V What are the values of a that will make: Y a. (X,X) a Nash equilibrium (NE)? b. (X,Y) a Nash equilibrium (NE)? c. If a=-1, set-up the linear programming models that will solve the mixed Nash equilibria of the given game.
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- Consider the attached game depicted in Normal Form. Find one Nash equilibrium and verify that it is a Nash equilibrium. Note: 1. Remember to express the Nash equilibrium in the form of a strategy profile. 2. Use the definition of Nash equilibrium to verify that the strategy profile you find is really a Nash equilibrium.Question 5 Consider the following Extended Form Game: A' (1,1) A P2 B' O [(B, B')} (2,3) O ((B.(B',A')). (B.(B¹, B'))) P1 A' What is the set of Nash Equilibria? O {(B.(A', B)), (B,(B', B'))) (4,5) B O ((B.(A'A')). (B.(A, B')). (B,(B,A')), (B,(B', B'))} P2 B' (6,7)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 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 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats 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. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 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 they agree upon, if any? a) Both…
- 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 Left Right (3, 1) (5,7) (4, 3) Center (1, 4) (2, 2) (3, 2) (6, 2) (4, 6) (5, 5) Up Middle Down Which of the following outcomes represents a Nash equilibrium in the game? (Up, Center) (Middle, Right) (Down, Left) (Down, Center)6) The following is a static game D 2,2 0,3 D 3,0 1,1 a) Convert this game into dynamic form game b) Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. c) If you consider this game as dynamic then what kind of dynamic game is this.Find any Nash equilibria in the game below. Firm B Co-operate Don’t co-operate Firm A Co-operate 60 60 0 80 Don’t co-operate 80 0 10 10 a. There is one Nash equilibrium: both firms don't co-operate. b. There are no Nash equilibria. c. There are two Nash equilibria: one firm co-operates and the other firm doesn't co-operate. d. There are two Nash equilibria: (i) both firms co-operate and (ii) both firms don't co-operate.
- Problem 1. You are given the following bimatrix games. For each one, find all pure Nash equilibria. (a) (Prisoner's Dilemma) Player 2 Quiet 2, 2 3,0 Fink Quiet Fink 0,3 1,1 Player 1 (b) (Matching Pennies) Player 2 Нead Head 1,-1 Tails -1,1 Player 1 Tails -1,1 | 1, -1 (c) (Battle of the Sexes) Girl OK, football... OK, theatre... Football! Theatre! 1,5 0,0 0,0 5,1 Boy (d) (Battle of the Sexes... modified) Girl Football great, I will invite my dad Theatre! OK, football... OK, theatre... Football! 1,5 0,0 0,0 5, 1 0,0 -1 , 2 BoyThis 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)Answer all the questions, show all the working. Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.
- Find any Nash equilibria in the game below. Firm B Co-operate Don’t co-operate Firm A Co-operate 60 60 0 80 Don’t co-operate 80 0 10 10 Answer a. There is one Nash equilibrium: both firms don't co-operate. b. There are no Nash equilibria. c. There are two Nash equilibria: one firm co-operates and the other firm doesn't co-operate. d. There are two Nash equilibria: (i) both firms co-operate and (ii) both firms don't co-operate.Which of the following statements about a Nash equilibrium is not correct? A. Each player plays a best response to opponents' Nash strategies. B. No player has a profitable unilateral deviation. C. For each finite noncoopertiave game there always exists a pure strategy Nash equilibrium. D. A game has at least two players. Which one of the following statements is incorrect? A. For dynamic games with complete information, not all subgame perfect Nash equilibrium points can be found by backward induction. B. A finite dynamic game with complete information may also have a normal form representation. C. A finite static game with complete information may not have a pure strategy Nash equilibrium. D. A finite static game with complete information cannot have an extensive form representation. Which one of the following statements is correct? A. A supergame cannot have any subgame perfect Nash equilibrium. B. A supergame can only have finite number of subgame perfect Nash…Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.
