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Q, Please sold the Unique baysian Nash equilibrium and the mixed strategy nash equilibrium
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p1/p2 |
u |
n |
|
a |
8,8 |
8,2 |
|
b |
0,8 |
10,10 |
|
c |
8,8 |
9,2 |
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- q60c- Is the Nash equilibrium the best outcome for this problem? ExplainJagtar and Ravi both grow mangoes, which they sell in the same local market. They are deciding whether to pick 5 baskets worth of mangoes or 10 baskets, and have the following profit matrix: Jagtar 5 1 17 5 1 22 16 14 Ravi 1 24 14 a. What is the Nash equilibrium if both individuals make their decisions simultaneously? b. Does your analysis change if the local market charges a lump-sum fee of 12 to set up a stall and sell the mangoes in the space it provides? c. What would happen if the local market were instead to charge a lump-sum fee of 18?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.
- Consider the lollowing extensive form game. P1 P2 P2 7. 1 7. Find the Nash equilibrium Find subgame perfect Nash Equailabrium. Explain why all Nash equilibriums are not subgame perfectwhy is a nash equilibrium stableNASH EQUILIBRIUM Consider the following game in strategic form. bị b2 a1 16,12 4,20 a2 6,28 9,14 a3 8,6 12,4 1-T-0 1-T The Equilibrium Existence Theorem guarantees that this game possesses at least one Nash equilibrium of the form (7* , o*, 7*). Which values of T are part of such an equilibrium? (Mark all values for which an associated equilibrium exists.) Select one or more: 0.00 0.60 0.30 0.80 0.25 0.75 0.20 O 1.00
- Consider the following normal form game Player 2 L C R Player 1 U 5, 4 4,5 3,8 8,3 8,0 5,5 6,3 0,8 M D 8,8 Find all the pure strategy Nash equilibria of the game.Q2. For each of the following extensive form games, identify the subgame perfect Nash equilibrium. Game 5 Game 6 9. 15 10 10 Game 7 {:) 10 11 101) Consider the following game. 1 \ 2 A B D 4,2 2,2 5,1 E 4,1 3,5 7,3 F 5,2 4,4 7,0 G 5,4 0,4 3,0 a) Given that o2 = G), 4 find BR,(02) '6' b) Find the set of rationalizable strategies profiles, R of the game. c) Find the pure strategy Nash equilibria of the game
- 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?Q3 Consider the following three-player normal form game (Player 3 is the page player): Player 3 A в Player 2 Player 2 A в A B 1,2, 3 в 2,3,1 Player 1 A Player 1 A 2, 1, 3 3, 2, 1 3, 2, 1 1,2, 3 в 1,3, 2 3, 1,2 For each player, strategies are A and B. a) Find the pure strategy Nash equilibrium of the above game. Assume now that the above game is played sequentially, with Player 3 moving first, Player 1 moving second, and Player 2 moving third. b) Write down the game tree. c) For each player, list all the available pure strategies. d) Find the subgame perfect equilibrium outcome and compare it with the equilibrium outcome you found in subquestion a). Comment.Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.