Many of my players express interest in "political intrigue," but I'm not really sure where to place power and what conflicts regarding it might be. The setting is a large, well-armed city that was founded decades ago as a prisoner colony of criminals who traded their remaining punishment for defending said city. The city itself is positioned in a mountain pass fronting a largely unexplored wilderness. Finally, I'm thinking of making it an independent city-state and/or influenced by multiple nations.
Since the majority of your populace have a criminal mindset, conflict is going to come pretty easy to them. Even given their freedom in return for their defensive contribution to the city, they are going to fall back on violence as a method for social climbing. It is what they know. The undercity (beneath the rule of law) will be a realm of extortion, thugery and assasination. Loyalties will be pretty obvious down at street level, but your players may still have challenges, negotiating a safe path for themselves among the gangs and warlords.
Meanwhile, the city founders (whom I'm assuming were not criminals) will want to pursue politics as usual with methods ranging from overt power-brokering, favor-trading and nepotism to covert but non-violent blackmail. This is the realm where conspiracies will florish, allowing your players to uncover the hidden motivations for the actions of the city's power elite. If they discover something juicy about someone very high in the tree, they might even be able to get into the game of manipulating the manipulators.
Where the two factions meet, there will be unifying conflict. The power elite will put aside their personal agendas to deal with an uprising from the unwashed masses. Meanwhile the warlords will parlay to mount an assault on the ivory towers. So the secret to keeping the intrigue alive is to keep the two factions from meeting. A strong police force would probably be enough to keep the city founders from getting scared, while simultaneously keeping the street gang warlords from getting ambitious.
The only other thing you need in this recipe is a little prosperity. For the same reason that war between the factions diminishes the opportunity for intrigue, a mutual enemy or shared threat (starvation) provides a similar unifying, intrigue killing force. So give the city a couple years off from any danger emerging from the unexplored wilderness, and let the chicanery begin!
Think about what intrigue is, which is typically a brutal - yet covert - competition, typically for power. Why does this situation arise?
- An established goal to compete for - if all your players what different things, there is no need to compete. Historically an imperial throne or political advantage for their faction are classic areas where intrigue arises. Tipping the political balance a little in favour of your faction may be just the thing you need to achieve a long-term goal.
- Powerful factions who want to achieve the goal - the groups or people who want to achieve the goal need to have sufficient power already that they can organise and engage in intrigue.
- Well balanced power bases - if someone has significantly more power than anybody else then there is little need for intrigue, because they can break cover. However, if everyone is evenly matched ( and/or playing their cards close enough to their chest that they all believe themselves to be evenly matched ) then they need to find more covert means to build secret alliances, expose one another's weaknesses and try to build sufficient power to achieve dominance.
- Potentially an instrument of balance a truly skilled political operator- a brilliant emperor or civil servant perhaps - can maintain power by allowing intrigue to divert their political adversaries' energies so they are focused on their own rivalries and not on overthrowing the people at the top. In this way it can be a valuable political tool for a leader who may not have as much financial clout as other members of the court but has managed to attain power through political flair or public popularity, the latter of course being another factor that can be influenced by intrigue.
If you think about the environment that intrigue creates it is one where everyone is playing for advantage against everyone else. This is typically based around mistrust, rumour and shifting alliances which only last as long as they serve both parties involved- the moment someone can gain advantage by selling out a current ally, they will. Everybody lies at least some of the time. New players appearing on the scene will be immediately interesting to all the players around because of how they can influence the balance of power- small advantages over a long time can be sufficient to alter things in any faction's favour.
You could takes some lessons from history - Rome and later the Byzantine Empire were great homes of political intrigue, as were the Italian city-states of the medieval period and the renaissance which- among many others, gave us the Borgias and the Medici, while the courts of the Chinese imperial dynasties were no less intrigue-ridden. You can find interesting examples going back from the early days of recorded history right up to modern politics. In fiction there are a lot of great examples to take inspiration from - George R R Martin is a classic example, but Guy Gavriel Kay and Dorothy Dunnett are personal favourites of mine for constructing complex political situations where characters weave webs of intrigue to overthrow their enemies.