solution

There are two gas stations in a certain block, and the owner of the first station knows that if neither station lowers its prices, he can expect a net profit of $100 on any given day. If he lowers his prices while the other station does not, he can expect a net profit of $140; if he does not lower his prices but the other station does, he can expect a net profit of $70; and if both stations participate in this “price war,” he can expect a net profit of $80. The owners of the two gas stations decide independently what prices to charge on any given day, and it is assumed that they cannot change their prices after they discover those charged by the other

(a) Should the owner of the first gas station charge his regular prices or should he lower them if he wants to maximize his minimum net profit?

(b) Assuming that the profit figures for the first gas station apply also to the second gas station, how might the owners of the gas stations collude so that each could expect a net profit of $105?

Note that this “game” is not zero-sum, so that the possibility of collusion opens entirely new possibilities.