What happens with research when there is a 2 vs 1 game in Civilization 5?

Solution 1:

Short Answer: The team of 2 has their technologies cost 1.5x normal, but all things being equal (if they each have identical cities to the single player) they produce 2x the Science output giving them an expected research rate of 133% normal (they can research things in 75% of the time).

Longer Answer: Generally, the cost of technologies seems to be multiplied by (0.5 + (0.5*n)) where n is the number of players on a team. For example 4 players makes it cost (0.5 + 0.5*4) = (0.5 + 2) = 2.5 times the normal amount. Note this does not completely balance out the fact that the team produces n times the science output.

I tested this using hotseat games, with all players as Humans on Prince difficulty. I looked at the Science cost of Pottery (one of the first techs) and Future Tech (the last tech). I checked this quick and standard gamespeed.

Quick gamespeed

1 player - Pottery 25 FutureTech 6,684
2 players - Pottery 36 FutureTech 10,025
3 players - Pottery 49 FutureTech 13,367
4 players - Pottery 60 FutureTech 16,708

Standard gamespeed

1 player - Pottery 46 FutureTech 12,597
2 players - Pottery 69 FutureTech 18,896
3 players - Pottery 92 FutureTech 25,194
4 players - Pottery 115 FutureTech 31,493