In the Editor there is a "simple game mechanism" called "Difficulty Levels". You can reduce the Corruption here to 0% if you want. You can have a "runaway game" if you choose. That is a way to "Deal with that"!
May be better to say, that is one part of "to deal with that". When looking in the C3C online-help, you can see the following:
Difficulty levels page:
Determines the percentage of normal corruption experienced on the selected difficulty level. The default is 100% on all levels, meaning corruption will affect city production and wealth as it normally does in Civilization III. Setting this value lower or higher will reduce or amplify corruption proportionally.
NOTE: The Corruption Modifier has no effect on players whose government experiences catastrophic corruption, cities in civil disorder, or capital cities. In these situations, corruption is automatically set and no formula is calculated.
As it is the "catastrophic" and "rampant" corruption (=RANK CORRUPTION), that is really annoying for gameplay in C3C, here the slider in the "Difficulty Levels" doesn´t help.
Therefore more important is the setting of the
"Optimal Number of Cities" in the World Size Properties:
From the C3C online-help: (This setting) Determines the optimal number of cities before rampant corruption occurs. If a player exceeds this number of cities, corruption dramatically increases, regardless of how far away from the capital a city is. Setting this value higher reduces the effects of corruption; lower values increase them. On a standard 100 x 100 map, the default is 16.
I hope this helps a little bit.
