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4. There is a $1 bill that Mary, Sam and David wants to share. Unfortunately, $1 is the smallest bill and it cannot be divided. Therefore, only one of them will get the $1 bill and the remaining players wont receive any money. Mary proposes the following procedure. Each of them will simultaneously and independently write 1 or 2 on:a paper. Then, papers will be collected and the numbers that are written by each will be added up and divided by 3. If the remainder is zero, Mary will get the $1, if the remainder is one, Sam will get the $1 and if the remainder is two, David will get the $1. (That is, for example, Mary writes 1, Sam writes 1 and David writes 2, the sum is 1 +1+2- 4 and hence remainder when divided by 3 is 1. Therefore, Sam will get the $1 bill.) (a) Exhibit this situation as a normal form game (matrix) (b) Find all the Nash equilibria, if any

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