Three department stores, A, B, and C, simultaneously decide whether or not to locate in a mall

Question:

Three department stores, A, B, and C, simultaneously decide whether or not to locate in a mall that is being constructed in town. A store likes to have another with it in the mall since then there is a critical mass of stores to induce shoppers to come out. However, with three stores in the mall, there begins to be too much competition among them and store profits fall drastically. Read the payoff matrix as follows: the first payoff in each entry is for A, the second for B, and the third for C; C€™s choice determines which of the bold boxes the other players find themselves in.

a. Find the pure-strategy Nash equilibrium or equilibria of the game. You can apply the underlying method from the text as follows. First, find the best responses for A and B, treating each bold box corresponding to C€™s choice as a separate game. Then find C€™s best responses by comparing corresponding entries in the two boxes (the two entries in the upper-left corners of both, the upper-right corners of both, etc.) and underlining the higher of the two payoffs.
b. What do you think the outcome would be if players chose cooperatively rather than nonecooperatively?