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Let X be your income, Y your opponent's income, and S some income amount.
Assume that Y > S, X + S > Y, and S > 0.
Then (X + S)/Y < X/(Y - S).
In other words, the ratio of your income to your opponent's income is better if you deny your opponent S income rather than increase your income by S, given the assumptions. And the assumptions are pretty reasonable here...if Y > S is false then the problem is ill-defined (Y - S is negative). If X + S > Y is false then you're probably in trouble, and the situation is reversed (you want the income rather than denying your opponent the income).
Although denying income is better than gaining an equal amount of income in most cases, it's probably more difficult to achieve since you have to control territory closer to your opponent's unit production / commander.
It's worth noting that wagons can allow you to deny your opponent income if you reach a part of the map first, and denial of income is a great way to generate value. I'd even argue that denying income is more effective than increasing your own income, because you're taking away the flexibility your opponent has.
Great guide. I recommend everyone who wants to play multiplayer to read this guide.