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The value of x is 0<x<90. For what value of x is (D, R) a risk dominant equilibrium.
Game
Bob
L R
Ann U 100,100 0, 0
D x, x 90, 90
Select one:
a.
none of the other answers.
b.
It is never risk dominant.
c.
For all x, where 0<x<50
d.
For all x, 0<x<90.
e.
It is always risk dominant
Step by step
Solved in 3 steps
- A st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.1. What is the expected value of playing this game ? a. The player repeatedly rolls a six - side d die until it comes up 6. b. When the die comes up 6 , the player receives a payoff, and the game ends. The player get s precise ly one payof f. c. The initial payoff is $6, and it increases by 20%. The f irst roll payoff is $6 ; the second roll payoff is $7.20 (1.2*$6) ; the third roll payoff is $8.64 (1.2*$7.20), and so on. What is the expected value of playing this game?3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760
- 2. B Left Right Up 1, 3 3, 1 A Down 2, 2 4, 4 a. Find the Nash equilibrium or equilibria b. Which player, if any, has a dominant strategy? с. Does A benefit from changing the game by reducing his or her payoff in this way?3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 8Question 1 Bob. Ann north Consider the following sequential-move game between Ann and Вов south visky ир down (2,6) Ann Nature left 50% (2,5) cold hot left 50% (3,10) right 50% (56) (3,4) (4,7) External uncertainty is handled by an outside player called "Nature". Nature chooses "Left" with probability 50%, "Right" with probability 50%. A. Use backward induction to find the rollback equilibrium. B. What are the rollback equilibrium payoffs? C. How many strategies does each player have? For each player, list all his/her strategies.
- Micro Nash game theory Consider the game matching pennies with an external option u for player 1. Suppose that u in ]0, 1[. H T H. 1, -1 -1,1 1, -1 T -1,1 й, 0 й, 0 a. Calculate the best response apps for each player. b. Give the set of Nash equilibria for the game.1\2 U D L 4,3 0,0 R 0,0 2,1 C 1,4 0,0 Q. Suppose players 1 and 2 play the stage game depicted above. Check whether each of these strategies constitute a SPE? 1. Play U,C in Rounds 1 and 2 2. Play D,R in rounds 1 and 2 each 3. Play U,L in Round 1 followed by U,C in Round 2. If Player 2 defects punish by playing D,R in round 2. 4. Alternate between U,C and D,R in Rounds 1 and 21. Repeated Game Consider the following normal form game. D Player 1 E F A 10, 10 -12,-1 15, -1 Player 2 B -1, -12 8,8 -1,-1 C -1, 15 -1,-1 0,0 (a) Suppose this game is played once. Find all pure strategy Nash equilibria. (b) Now suppose the game is played two times without discounting. Find all strategy profile that can be played in the first period in a SPNE. (c) Now suppose the game is played T times without discounting, where T is a finite number. Find the smallest T such that (E,A) is played in the first period. (d) Now suppose the game is played infinitely many times and the players have a same discount factor 8 < 1. Find the smallest d that can support the SPNE in which (D,A) is played in every period along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as a punishment).
- 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?on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.0,0 not 4, 10 b advertise Good seller Select all true statements. n Nature Consumer -1,0 Bad seller b -1,-5 advertise n not -6,0 0,0 a. There is a separating equilibrium in this game in which only the good seller advertises. b. There is a separating equilibrium in this game in which only the bad seller advertises. c. There is no separating equilibrium in this game.