Player 2 Left Right P1: $4 Player 1 Up P2: $1 P1: $10 Down P2:s10 Which of the Nash Equilibrium to this game are efficient? [Check all that apply] A) (up, left) B) (down, left) C None are efficient (D) (up right) E (down, right) Last saved 4:31:15 PM P1:S1 P2: $6 P1: $0 P2: $11 Grading
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![Player 2
Left
Right
P1: $4
Player 1
Up
P2: $1
P1: $10
Down
P2:s10
Which of the Nash Equilibrium to this game are efficient? [Check all that apply]
A) (up, left)
B) (down, left)
C
None are efficient
(D) (up right)
E
(down, right)
Last saved 4:31:15 PM
P1:S1
P2: $6
P1: $0
P2: $11
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- rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.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. None1. Nash Equilibrium (a) Find all pure Nash Equilibria P1/P2 W X Y Z 9,9 0,7 5,5 1,1 7,0 0,0 4,2 7,7 5,5 2,4 0,0 1,1 1,1 7,7 1,1 0,0 A B C D (b) Consider the following picnic game. There are N players in the game each who can chose to bring food to the picnic or not. Let b;= {0, 1} be player i's choice of bringing food with 0 as not and 1 as yes. If they decide to bring food it comes at a cost c;(1) = 1 and no cost to bring food. Payoffs are sum of food brought minus individual cost. i. Write out the normal form matrix if N = 2 ii. If N = 2 find all pure Nash Equilibria iii. Find all pure Nash Equilibria in the general game
- Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.Во ein g C. 190 d. 210 Inv est Do n't Diagram 1 Air bus Air bus Inv est Do n't Inv est Do n't (-25,-25) (170,0) (0,190) (0,0) Suppose that both Boeing and Airbus receive a subsidy of 20 units to invest. What is Boeing's equilibrium payoff in this game? a. -5 b. 0Aedri 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…
- QUESTION 9 D 2 C D D, D OD, C C, D C II C (2,2) (4,0) (0,4) (3,3) In the dynamic game represented by the graph above, the numbers inside paranthesis show the payoffs of Player 1 and Player 2, respectively. The Nash equilibrium of this game is for Player 1 to choose O C, C and Player 2 to chooseSuppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0. -3 1 1. раper scissors -1 -1 3 (a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium 3'31 for this modified 3'3 game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
- ROWENA 2 Answer 1: 2 Answer 2: 2 Answer 3: 1 Earth Water Wind Answer 4: Fire of the Nash equilibrium, (Rowena's 1 Colin's 3 3 North 1.3 This simultaneous game has two Nash equilibria. The Nash equilibrium, (Rowena's 2 , Colin's 1,2 3,2 2,0 COLIN South 3,1 1,2 2,1 3,0 East 0,2 2,3 1,1 West 1.1 1,1 0,3 2,2 ) has a greater joint payoff than thatWhat is the Nash Equilibrium of the following game? |0, 0 Up Down 3, 2 |2, 1 3, 1 2, 6 4, 2 5,5 10, 0 a. (Down, D) b. (Down, C) c. (Up, A) d. (Up, B)Во ein g Inv est C. 25 d. 200 Do n't Diagram 1 Air bus Air bus Inv est Do n't Inv est (-25,-25) (170,0) (0,190) Do (0,0) n't Suppose that both Boeing and Airbus receive a subsidy of 30 units to invest. What is Boeing's equilibrium payoff in this game? a. 0 b. 5