Before you understand the best ways to increase intrigue, you have to understand how intrigue works.
To gain intrigue, you must to preform a covert operation on the city specified to boost it. The harder and riskier the quest, the more intrigue you can earn (for that city).
A city has a minimum intrigue level of 0 and a maximum of 5. The higher level of intrigue the city has, the more difficult missions will be unlocked.
You have 10 possible missions:
1. Establish Network: Very Easy. Gathers various pieces of information about the target city and player, and displays the information in a window adjacent to the city while in covert operations view. The amount and detail of the information increases with the performing agent’s level.
2. Siphon Energy: Easy difficulty. Diverts energy resources from the target city to the player.
3. Steal Science: Easy difficulty. Diverts science resources from the target city to the player.
4. Steal Technology: Moderate difficulty. Steals a technology from the target player. This doesn’t necessarily match a tech that the target player has. One is automatically selected that is an appropriate reward.
5. Hack Satellites: Moderate difficulty. Deorbits a random satellite.
6. Call Worm Strike: Hard difficulty. Draws hostile aliens to the target city. This operation is allowed only by the Harmony Affinity level.
7. Dirty Bomb: Hard difficulty. Decreases the target city’s population substantially. This operation is allowed only by Purity Affinity level.
8. Sabotage: Hard difficulty. Pillages nearby improvements. This operation is allowed only by Supremacy Affinity level.
9. Recruit Defectors: Moderate difficulty. Gives the player a set of random military units at their capital.
10. Coup D’etat: Moderate difficulty. Transfers control of the target city to the performing player.
And now for the tips on boosting a city's intrigue:
Agent Rank. These two words will change how you play covert ops in the game.
So you have your agents, gaining a cities intrique from doing these missons to boost the intrigue of the enemy city, but your agent's are getting a special reputation while doing it. They are boosting their rank, which gives them more of a chance to succeed in the later missons. This is a key advantage, you can basically grind low level missons on city's all over to boost your Agent's rank and it will greatly help your chance of succeeding in a mission.
The higher your Agent's rank, the more likely his covert ops misson will be successful.
Be aware that even with the lower ranked missons, your agent will always have a chance of being killed during the misson. Try playing strategically, and you will be able to do a
Coup D'etat in no time.