Three player difficulties

I am working on the "Gateway" version of Normannia--have played twice, seems to work despite being on a larger board (33 areas) to accommodate the bigger diceless version. Now I'm looking at a three player version, but whenever I do this I seem to run into problems with nation interaction. It's very difficult to avoid strange interactions with three players. It reminded me of the "four color map" problem.

"The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent only if they share a border segment, not just a point. Each region must be contiguous (http://en.wikipedia.org/wiki/Contiguity): that is, it may not have exclaves (http://en.wikipedia.org/wiki/Exclave) like some real countries such as Angola (http://en.wikipedia.org/wiki/Angola), Azerbaijan (http://en.wikipedia.org/wiki/Azerbaijan), Italy (http://en.wikipedia.org/wiki/Italy), the United States (http://en.wikipedia.org/wiki/United_States), or Russia (http://en.wikipedia.org/wiki/Russia)."

http://en.wikipedia.org/wiki/Four_color_theorem

I'm trying to do the same to accommodate just three players, and it's very difficult to do. Even without the "petty diplomacy problem"--that one player, if he decides he cannot win, can determine which of the other two can win--it makes three player strategic map-based games difficult in general.

There are ways to overcome the petty diplomacy problem, and if you have just three nations you can have three players, but when you start trying to use many nations, it becomes really difficult to do well.