Two people are engaged in a joint project. If each person i puts in the effort xi, a nonnegative number equal to at most 1, which costs her c(xi), the outcome of the project is worth f(x1, x2 ). The worth of the project is split equally between the two people, regardless of their effort levels. Formulate this situation as a strategic game. Find the Nash equilibria of the game when (a) f(x1,x2)= 3x1x2 and c(xi) = xi^2 for i = 1, 2, and (b) f(x1, x2) = 4x1x2 and c(x) = xi for i = 1, 2. In each case, is there a pair of effort levels that yields both players higher payoffs than the Nash equilibrium effort levels?

Rate of return, standard deviation, coefficient of variation personal finance problem mike is searching for a stock to include in his current stock portfolio. he is interested in hi-tech inc.; he has been impressed with the company's computer products and believes hi-tech is an innovative market player. however, mike realizes that any time you consider a technology stock, risk is a major concern. the rule he follows is to include only securities with a coefficient of variation of returns below 1.07. mike has obtained the following price information for the period 2015 through 2018:hi-tech stock, being growth-oriented, did not pay any dividends during these 4 years. a. calculate the rate of return for each year, 2015 through 2018, for hi-tech stock. b. assume that each year's return is equally probable and calculate the average return over this time period. c. calculate the standard deviation of returns over the past 4 years. (hint: treat this data as a sample.) d. based on b and c determine the coefficient of variation of returns for the security. e. given the calculation in d what should be mike's decision regarding the inclusion of hi-tech stock in his portfolio?