Consider the following extensive form game: Find the subgame-perfect equilibrium for this game. Player 3RPlayer II 1,2| 1,2,0Player2Player 2BI 1,2,0| 1,0, 2,$(2,±,\)

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Answered: Consider the following extensive form…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let's consider the following game: Player 1 chooses a (potentially negative) number x, and player 2 chooses a (potentially negative) number y. The payoff for player 1 is given by U1 = 100x - x2 - 2xy. The payoff for player 2 is given by U2 = 130y - 2y2 - 2xy. Solve for the Nash equilibrium in pure strategies. What is Player 1's payoff in the equilibrium? Enter a numerical answer below. You may round to the second decimal if necessary.
For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. For row player R: r2 = For column player C: C1 = C2 = Find the value v of the game for row player R. V = Who is the game favorable to? The game is favorable to the row player. The game is favorable to the column player. This is a fair game.
Consider the following sequential game between two players: 1 and 2. In stage 1, player 1 makes a choice beteeen A and B; in stage 2, player 2 makes a choice between C and D upon observing player 1l's choice in stage 1. Suppose the player's payoffs are given as follows: Outcome A,C A,D B,C B,D Fully characterize which is the formal algebraic formulation of the game Payoff Pair 3,4 1,3 1,3 3,3
Consider the following normal-form game. A B C T 1, 1 2, 2 3, 4 9, 3 B 2, 5 3, 3 1, 2 7, 1 Find all pure Nash equilibria and one mixed Nash equilibrium of this game.
1. Consider the following symmetric game. Find all evolutionarily stable strategies (pure and/or mixed). P2 S1 S2 S3 4,9 | 0,3 0,0 | 0,3 3,0 3,0 2,2 S1 1, 1 P1 S2 9,4 S3
Decide whether the game is strictly determined. If it is, give the players' optimal pure strategies and the value of the game. в a 1 1 A 3 -5 a. A's optimal strategy is a; B's optimal strategy is q; value: 1 b. A's optimal strategy is b; B's optimal strategy is p; value: 1 c. A's optimal strategy is a; B's optimal strategy is p; value: 2 d. A's optimal strategy is b; B's optimal strategy is q; value: 0.5 e. The game is not strictly determined
15 For the given Bayesian Game, determine the average payoff for a hardworking (H) teacher for Interested (I) type of students with strategy Not Study (NS) and Not Interested (NI) type of students with strategy Study (S), i.e. Teacher's payoff for strategy (H,(NS,S)). Player-1: Teacher, Player-2: Student Student may be of two categories: INTERESTED (I) or NOT INTERESTED (NH) with probability 1/2. Action of Teacher: Hard work (H/ Laty (L) Action of Student: Study (S)/ Not Study (NS) Game Table: P(I)=1/2 Teacher\ Student NS H. 10,10 0,0 L 5,5 5,0 P(NI)=1/2 Teacher\ Student S NS 5,5 0,5 10,5 5,10
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In the strategic form game below: (a.) What is P1's best response to each of P2's strategies. (b.) Find all Pure Strategy Nash Equilibria (PSNE). Show all work. (c.) Show an example of a Mixed Strategy Nash Equilibrium (MSNE) in this game. How many are there? Explain. Hint: we can assign probabilities of 1 or 0 if a player chooses a given strategy with certainty in a MSNE. Show your work. Player 1 a b с d Player 2 W X Y Z 0,5 1,3 1,7 0,8 1,6 0, 2 2,6 0,7 0,5 1,3 0,8 3,9 1,2 0,4 0,4 3,5
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b) Briefly explain the sense in which a Nash equilibrium corresponds to a "no regret outcome."
Consider the folliwng 3 x 3 two player normal form game that is being repeated infinite number of times. The strategy for player 2 is to play Z all the time. Player 1 is confused between two strategies: (i) play C all the time, and (ii) play A all the time. The discounting factor for player 1 is ố1 = 0.52 and the discounting factor for player 2 is 82 = 0.51. X Y (31 , 31) (41 , 90) (36 , 31) (33, 22) (18 , 36) (26 , 53) A (35 , 56) C (26 , 15) (41 , 69) a. Find the total discounted utility for both player 1 and player 2 if player 1 decides to play the first stratgy (playing C all the time). [ b. Find the total discounted utility for both player 1 and player 2 if player 1 decides to play the second stratgy (playing A all the time). c. Out of these two strategies, which one should player 1 choose? Why? (Use maximum 3 sentences)

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