3. Player 1 has a car which he wants to sell and there are two buyers, Player 2 and Player 3, who wish to buy it from him. The car has no value to Player 1 but Player 2 values it at ? units and Player 3 at 10 units. One or both buyers may make a bid for the car, and if both make a bid, the car goes to Player 3 since he values the car most. Let 1:00 be the totaiprot that all member in K, where K is a subset of the set of players, make through this sale. Thus, for example, a({1, 2}) = 17 since if Player 1 sold the car at price p, then he makes a prot of p and Player 2 makes a prot of F p. Note that for a prot to have been made, a sale must taken place; thus, for example a({2, 3}) = [J since no sale is made between the buyers. {a} Express v{.) as a mction of K and prove that it is a characteristic function. [b)ls the game essentiai? Explain. {c} Reduce the game into one in 0-iform. Use this new game to determine if this game has a non-eiapor core. (d) Determine the Shapiey vaiae of each player and interpret these values with respect to the power each player can exert on the outcome of the sales