How other cities in the Empire react largely depends on how high the leader of the other city thinks of you. If he admires you, you'll likely get a gift from him sometime. If he hates you, he will invade you sooner or later if he's your rival. There are some things you can do to improve favor with another city, but those are dealt with in the Gifts & Requests page.
You can see a city's favor towards you by going to the Empire map and clicking on a city. Favor is measured in 'points', which range from 0 to 100, 0 being absolute hate towards you and 100 being absolute love and devotion. The city's initial favor to you is set by the mission designer. If nothing is done, the favor level of a city will slowly drift towards a 'stable point', which is 50 for normal difficulty, with the rate of 1 point per half year or 2 points per year. However, you can't see the actual points in the game, instead, you'll have to do with rough descriptions like apathetic, furious and helpful.
The following table lists those favor levels and their associated point range:
|Favor "points"||Favor level|
|If you recently have...|
|greatly pleased them||Docile||Philanthropic||Philanthropic|
|greatly angered them||Hostile||Resentful||Rebellious|
The last 2 rows of favor 'levels' are only displayed if you recently have greatly angered/pleased a city. This usually triggers them into some action. When you've pleased a city, that action will almost certainly be giving you a gift of goods in the near future. When you've angered them, you can expect an invasion of a rival, a broken alliance from an ally, and a rebellion from a vassal.
Opening Trade and forming Alliances
Before a rival city will give in to your request to open up a trade route or form an alliance, that city must have at lease a certain favor level with you. For opening trade, that level must be 51 or above. So any city with favor respectful and above will immediately agree. If the city is apathetic towards you, it may or may not open trade, it depends. For more information regarding opening trade and benefitting from trade routes, read the article on trade.
Forming alliances is most of the time not necessary. However, forming an alliance has its benefits: you will be able to request defensive aid and strikes on another city, the city will be more favorable to you when you request goods (you can ask more before the city becomes annoyed), and perhaps the most important benefit: it won't attack you. To form an alliance with a rival, your favor with that city has to be at least 70, so an agreeable or admiring rival will always respond to your request for an alliance.