Gillette and Schick are two of the dominant manufactures of disposable razors worldwide. Each firm can either sign or not sign an exclusive contract with Hugh Jackman to appear on their TV ads. If both companies manage to sign with Jackman, they will each make $7 million in economic profit. If only one of them signs, it earns $10 million in economic profit and the other firm incurs an economic loss of $1.5 million. If neither firm sign, they only make normal profit.

Build the pay-off matrix for the above game. Identify "Nash Equilibrium", if any. Is this equilibrium optimal for both companies? Justify your answer.