Consider the stage game below. The game is repeated once (i.e. played twice). Find all the SPNE in pure strategy of that game. Make sure to explain why you ruled out some of the non-Nash profiles.
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- ITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)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?Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.
- MIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 18,2 80,60 a2 40,60 2,18 1-п 1-0 This game has a mixed strategy Nash equilibrium (T*,o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)MIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 19,1 80,70 a2 40,50 1,19 1-п 1-0 This game has a mixed strategy Nash equilibrium (7*, o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.) Answer: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.
- 8.1 Consider the following game: Player 1 A B C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1.1 E 0,0 1,1 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..9 00 3 -2 -8 A = ( ) and B = 03 -5 -2 Let I be the bimatrix game whose payoffs are described by A for the row-player and B for the column- player. 1. Compute all mixed Nash equilibria of T. 9Help me please
- INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. bị b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of d such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)Consider the following 2-person game, Player 2 A C А 3,3 1,1 0,0 1,1 2,2 0,1 0,0 1,0 0,0 Player 1 B C a) What would you recommend to a player who intends to play action? b) What are the Nash equilibria of the game? c) If you were asked to give a prediction as to what two people playing this game would do, what is your prediction? Why?Convert into Normal-Form Game and Find out the subgame-Nash Equi- libria? OUT (0, 2) Small Entrant Small IN Entrant Incumbent Large Large Small Large (−6, −6) (−1,1) (1,−1) What does the Information set imply in this game? (-3,-3)