question shows below:

Problem 5 (bonus). Consider a continuous version of the previous game: Players pick 11,?) E [0, 1] and the payout is |u 0|. (a) If Player I plays at a uniform point, what is the expected payout if Player 11 plays at v (as a function of 1))? What are the optimal 1)? (b) If Player II plays at a uniform point, What is the expected payout if Player I plays at u (as a function of u)? What are the optimal u? (c) Find strategies for the two players that guarantee an expected payout of 1/2 against any response