der “Providing a Public Good under Incomplete Information" -lecture notes.) If c, and c, have the following distribution. 0.5 1.2 C2 0.5 1.2 Prob 1/2 1/2 Prob 1/3 2/3 all Bayesian Nash Equilibria of this game. et all correct amswers.
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- Consider the game "Battle of the Sexes" as below. In the mixed-strategy equilibrium, Roger chooses to watch a movie with the probability y* of: Roger 0.5 1/4 3/4 1/3 Watch soccer Watch a movie Michelle Watch soccer 3, 1 0,0 Watch a movie 0,0 1,3Consider the job market signaling game given the figure below. The worker has two types: H and L, and q is the probability associated with type H. The production functions and indifference curves are as shown in the figure. In a pooling Perfect Bayesian Equilibrium of this game, the range of values possible for equilibrium level of education, Epool is (with an appropriate set of beliefs): (a) e1 only. (b) [e1, e3] (c) [e1, e2] (d) [e2, e3].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.
- can we find nash equilibrium through mixed strategy as well?Please draw or illustrateIn 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
- The purchase patterns for two brands of toothpaste can be expressed as aMarkov process with the following transition probabilities: Which brand appears to have the most loyal customers? Explain.c) Calculate the covariance and correlation of coefficient for the above stock. d) Is the above stock being a good combination in the portfolio? Justify. Note: Type clearly ans noPolice plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations L1, L2, L3 and L4 are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations. (1)what is the probability that he will receive a speeding ticket? (2)lf a person has got a speeding ticket, what is the probability that he speeded at location L3?
- rr.12.15 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 5,10Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations L1, L2, L3 and L4 are operated 30%, 40%, 20%, and 10% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, a) The probability that he will receive a speeding ticket is Blank 1 b) If the person received a speeding ticket on his way to work, the probability that he passed through the radar trap located at L3 Blank 2 (round off your answer to four decimal places)