To me, any political game - truly political game - needs to be built from the resources up. The essence of politics is "how do we divide a limited number of resources among people who a) all want more than we have and b) don't want to just murder people". Everything that you do in politics is really negotiating that resource division question, whether the resources in question are land and tons of grain, or sparkly magic powder, or the favor of the Crown (or other equivalent social intangible resources).
So, you have to have a) limited commodities that every faction needs, b) limited commodities that each (but not every) faction has a source for, c) mutually agreed upon procedures for negotiating for these resources that you don't have using the resources that you need, and d) a schedule of escalation that is reasonably well known, reasonably predictable, and which requires risk and cost to employ.
A are your resources in play. These can be solid, immutable things like land, they can be transferable things like money or trade goods or people, or they can be intangible but desirable like whatever proxies you want to use for respect or favor, or something like a 'vote' if you want a republic or corporate board setting.
B means that every faction (whether you're going for small-politics where every PC is a faction in and of themselves or something more traditionally L&L like houses or families or guilds) has SOMETHING to bring to the table that they can use to negotiate for the things that they need but don't have. Every faction needs to have power, but they shouldn't have the SAME power, and no faction should have all the things they need as a stable entity. Stability kills political pressure.
C is both your IC setting culture AND your procedural help files - ideally, there is a procedure up for 'how do I overthrow a leader I don't like' and 'how do I grab someone's land' and 'how do I create NPC pressure' BEFORE ANYONE ASKS, and that procedure is widely disseminated, universally available, and referred to regularly. Culture plays into it by setting boundaries for IC behavior which, again, should be aggressively referred to - if yours is an honor society, then define what 'honor' means for people of that setting, define where it comes into play, define how to get around it, define how to recover when you fail to get around it, and make it clear what you can (and can't) get as a reward for successfully navigating it.
And, finally, D is where you lay out the powers that each faction can bring to bear when things aren't going their way, ideally with levels of escalation and specific costs to use. What's worthy of a border raid (and how much does a border raid cost in soldiers/supplies/time), what's worthy of a trade embargo (and how is that likely to impact my own lands), what's worthy of a declaration of war (and how do we run a war anyway).
I think that without all four domains of this, any political game runs into a lot of problems, because people want to fall back on their own assumptions and, quite frankly, very few MU*ers know a thing about politics, state-level economics, or historical/historically inspired versions of either. The great thing about breaking it down like this, though, is that no one has to. You don't have to be realistic, you just have to be consistent and predictable.