A rumrunner attempts to smuggle rum into a country having two ports. Each day, the coast guard is able to patrol only one of the ports. If the rumrunner enters via an unpatrolled port, he will be able to sell his rum for a profit of $7000. If he enters the first port and it is patrolled that day, he is certain to be caught and will have his rum (worth $1000) confiscated and be fined $1000. If he enters the second port (which is big and crowded) and it is patrolled that day, he will have time to jettison his cargo and thereby escape a fine.
(a) What is the payoff matrix for the game? Denote the two ports by I and II, and write the entries of the matrix in thousands of dollars.
(b) What is the optimal strategy for the rumrunner?
(c) What is the optimal strategy for the coast guard?
(d) How profitable is rum running? That is, what is the value of the game?