Explain the .following questions as attached below.
Does this game have any pure strategy Nash equilibria? Part (B) is worth 30 marks. (C) Two California teenagers Bill and Ted are playing Chicken Bill drives his hot rod south down a one-lane road, and Ted drives his hot rod north along the same road, Each has two strategies: Stay or Swerve. If one player chooses Swerve he loses face: if both swerve, they both lose face. However. if they both choose Stay, they are both killed, The payoffs for the game of Chicken are given in the table below. Bill is the row player and Ted is the column player. Swere Find all pure strategy Nash equilibria. Lub Find the mixed strategy Nash equilibrium Min What is the probability that both teenagers will survive? Pari iCi is worth to marksQuestion 5. [18 marks] (a) Consider a 2-player game with the following payoff matrix. Here, the row player's strategies are 1, 12, and r3 and the column player's strategies are c1, C2, and C3. As usual, the row player's payoff is given first and the column player's payoff is given second in each cell. C1 C2 C3 1 (1,2) (0, 1) (2,3 12 (2,0) (1,2) (2, 1 ) 13 (0, 1) (0, 1) (1, 2) Does this game possess a pure Nash equilibrium? If so, list all pure Nash equilibria for this game. [4] (b) What does it mean for a 2-player game to be a zero-sum game? 3 Now, consider the following zero-sum game. The row player and the column player each simultaneously hold up 1 or 2 fingers. If the sum of the number of fingers both players hold up is even, the row player wins. If the sum is odd, the column player wins. The losing player pays the winning player an amount equal to the number of fingers the winner held up. (c) Give the payoff matrix for this game from the perspective of the row player. 5 (d) Formulate a linear program that gives the row player's optimal mixed strategy for this game (you do not need to solve this program). 61. In this exercise you will employ regression analysis to study how education, experience, and job tenure a'ect wage. First, consider the following regression model: lavage.- = 60 + lgradei + gttl_expi + ,83tenureg + at, To estimate this model, generate a new variable called lnwage which is the natural logarithm of wage times 100. (This will make it easier to interpret the coefcients. For example, a one unit increase in grade will correspond to a 1% increase in wage.) (a) Use the regress command to estimate the above model. What is the percentage change in wage when education increases by one year? How about job tenure? (b) To test the null hypothesis that {32 = 3, what is the t-statistic? What is the p-value? Will you reject the null hypothesis at the 10% signicance level? Next, to study if education has a quadratic (nonlinear) eect on Inwage, consider the following regression model: lavage; = 60 + Blgradeg + gttl_exp,- + gtenureg + igradef + as, To estimate this model, generate a new variable which equals grade? Use the regress command to estimate the OLS coeicients. (c) What is the value of 31? What is the 95% condence interval? (Use the standard normal critical value 1.960 to nd the condence interval.) (d) What is the value of 34? Is it statistically signicant at the 10% level? (e) For someone with 12 years of education, what is the percentage change in wage if she receives an additional year of education? (f) To test the null hypothesis that 61 = 64 = 0, what is the Bonferroni statistic? How many restrictions are in this hypothesis? What is the p-value? Will you reject the null hypothesis at the 5% level? STATA QUESTION clear all // clear the environment/memory set more off sysuse nlsw88 // load the built-in dataset nlsw88 2. In this exercise, you will conduct regression analysis with binary and categorical variables. (3.) Use the command tabulate to show the categories of the variable occupation and their frequencies. What is the relative frequency of the category Sales? Please report a number between 0 and 1. (b) Use the same command, this time specifying the option nolabel, to visualize the numeric values corresponding to the different categories of occupation. Which numeric value corresponds to the label Sales? ((1) Use the command summarize with the option if to compute the sample mean of wage for workers with Sales occupation. What is the average wage for workers with Sales occupation? (d) Use the command regress wage Loccupation to run a regression with binary variables for every occupation category. (Adding i. to a categorical variable will automatically generate a binary variable for each category.) The occupation with numeric value 1 is used as the base group. Given the regression results, what is the average wage for workers with Sales occupation? How does your answer compare to part 2(c)? (e) Which occupation has the highest average wage? How much is it? (f) Use a similar command as in step (d), this time to study the average hours for each occupation. Which occupation works the longest hours per week? How many hours on average for this occupation? Next, we follow a similar procedure as in steps (a)w(d) to study the wage gap among di'erent races. (g) Use the command regress wage 1 .race to run a regression with binary variables for every race category. What is the average wage for white? (h) What is the wage gap between white and black (report a positive number)? What is the 95% condence interval for this wage gap? (i) Generate three binary variables for categories in race to run a saturated regression instead of (g). What is the average wage for white? How does your result compare to (g)
