Assume the takeover is wise for n. The takeover is then unwise for
n+1, as the other companies now find themselves in the same situation
as you for n. If the decision is unwise for n, by similar reasoning
it is wise to takeover FD for n+1. Now note that for n=1 the takeover
decision is clearly unwise, hence by induction you should takeover
FD iff n is even.