After winning at Noble I made several attempts at Prince, but have failed every time.  Usually I get wiped out by an army of knights but in my last game I managed to survive till the end, until the leader (Victoria) won the space race.  After studying my rivals cities, I just don't think the computer is playing by the same rules as me. 

a) She had several cities with populations above 15.  How? With health and happiness constraints I can hardly go more than 10.

b) Most of the cities were full of farms, but I could see only few hammers and gold bags.  How, then, can she have massive armies and be way ahead in research?

c) If I declare war on one civ, I start getting unhappy citizens after 10 turns or so.  Yet, when Mansa declared war on me some time around 1700AD, he refused to make peace for 300 years and till 2015AD he was still at war with me.

My biggest complaint about the whole Civ series, and really it applies to many games where the AI has to make complex decisions: giving a simple decision algorithm (aka an "AI") more bonuses and cheats does not really constitute "higher difficulty."

Once I can beat the computer on level footing, I always seem to get bored with them.

I started a new game on Prince with Cyrus of Persia.  I got my capital city in one corner of land and Elizabeth was next to me and blocking my expansion.  I had no choice.  I attacked her with my Immortals.  I have taken London and York and eliminated her from the game.  I have some land for expansion but lot of desert.  Hatshestpur is next to me but I have restrained her from expanding into my territory with one more city.  It is 360BC and I have 5 cities now.  My score is 459, Hat is on 457 and Gandhi is somewhere, on 689.  My concern now is to produce more gold as my research rate is down to 50%.  I have all the resources I need and with stone I have built walls in my cities and plan to build the Hanging Gardens.  There is no such thing as the Great Wall in my game. My pop growth always gets restricted by Happiness resources.

Bye for now.

I had to go back a few years and replay the game.  After building the 5th city the economy was really dragging me down and my research rate dropped to 30%, which was untenable.

Instead of founding another city (Susa) I went back and, with stone, built the pyramid in my capital (Persipolis).  Now I can switch to Monarchy any time, as you have advised.  However, as Monarchy has a high upkeep and extra cost of more troops, I think I should build a few hamlets first to produce more gold.  I have built Libriaries and should build Lighthouses to work the sea tiles.  Then I can start increasing the population with the help of Monarchy?

Update on my game in 1665AD.

Gandhi is surging ahead on 2865 points.  I am second, with 1886 points.  He is building wonders like crazy.  I have pyramid, great lighthouse, hanging gardens and colossus. A Heroic Epic in one city is really useful. Gandhi has 12 cities to my 9.  Every game I play on Prince is like this, with one civ leading way ahead of the others.  Not much use being second best. I have built every improvement in all my big cities but cant catch up.  Any suggestions?

Isabella, the sourpuss, declared war on me across the sea, around 800AD and although I am sinking her ships, she wont give up. This is another oddity about this game as to why an AI player does not have citizens revolting from war weariness.