Question 4 (20 points). Lucy offers to play the following game with Charlie: \"Let us show dimes to each other= each choosing either heads or tails. If we both show heads= I pay you $3. If we both show tails= I pay you $1. If the two don't match= you pay me $2.\" Charlie reasons as follows. \"The probability of both heads is 1/(41 in which case I get $3. The probability of both tails is 1/43 in which case I get $1. The probability of no match is 1/2, and in that case I pay $2. So it is a. fair game.\" Is he right? If not, (a) why not, and (b) what is Lucy's expected prot from the game? Question 5 (25 points). Consider the following simultaneous-move game: Column (3) Find all pure-strategy Nash equilibria. (b) Suppose Row mixes between strategies U and D in the proportions p and (1 p). Graph the payoffs of Column's four strategies as functions of p. What is Columu's best response to Row's pmix? (c) Find the mixed-strategy Nash equilibrium. V's-That are the players' expected payoffs