In that test, buying the tech cost 193 gold, while researching took 128 beakers. So researching is more 'efficient' in that sense (though not in others).
But...
I had a look at how the cost varies with no. of civs you have contact with who have that tech. I did a test with 5 other civs, and one with 9 other civs. The details of what is going on are a little obscure, but essentially it works like this:
If no-one has the tech, you have to research the full quota of beakers (192 in the case of writing in my test). If you have contact with all the civs in the game, and they all have the tech, the cost in beakers is half of the full cost. In between it varies linearly. So if there are civs in a game, and you are in contact with M of them that have the tech, the cost in beakers is multiplied by (1-M/(2N)). So with 16 civs in game, 8 of whom you have contact with and who have the tech, then the cost to research it is reduced to 75% of the full cost. This is all for the cost in beakers of doing your own research.
The cost for buying the tech (ignoring slight variations due to the attitude of the civ you are bargaining with) is less, contrary to what I just said at the start of this post, UNLESS only one civ has the tech. Basically, the cost in gold is 3/4 the cost in beakers. But if 1 civ has a monopoly on the tech, the price you have to pay is doubled (1.5 times the cost in beakers).
There seem to be some other factors involved as well, but the above is pretty close. Here are some data for a test with 5 AI civs. First column is no. of civs I have made contact with, second is the cost in beakers to research the tech myself, lastly is the cost in gold to buy the tech of the Persians (who were annoyed with me - the price for polite civs was systematically 2 gold less).
0 192 -
1 175 260
2 155 116
3 136 103
4 117 90
5 96 76
The cost in beakers isn't exact, as it can't be determined precisely when you need 39 turns at 3 beakers per turn - it could be 117-119 with the same result (for example).
But...
I had a look at how the cost varies with no. of civs you have contact with who have that tech. I did a test with 5 other civs, and one with 9 other civs. The details of what is going on are a little obscure, but essentially it works like this:
If no-one has the tech, you have to research the full quota of beakers (192 in the case of writing in my test). If you have contact with all the civs in the game, and they all have the tech, the cost in beakers is half of the full cost. In between it varies linearly. So if there are civs in a game, and you are in contact with M of them that have the tech, the cost in beakers is multiplied by (1-M/(2N)). So with 16 civs in game, 8 of whom you have contact with and who have the tech, then the cost to research it is reduced to 75% of the full cost. This is all for the cost in beakers of doing your own research.
The cost for buying the tech (ignoring slight variations due to the attitude of the civ you are bargaining with) is less, contrary to what I just said at the start of this post, UNLESS only one civ has the tech. Basically, the cost in gold is 3/4 the cost in beakers. But if 1 civ has a monopoly on the tech, the price you have to pay is doubled (1.5 times the cost in beakers).
There seem to be some other factors involved as well, but the above is pretty close. Here are some data for a test with 5 AI civs. First column is no. of civs I have made contact with, second is the cost in beakers to research the tech myself, lastly is the cost in gold to buy the tech of the Persians (who were annoyed with me - the price for polite civs was systematically 2 gold less).
0 192 -
1 175 260
2 155 116
3 136 103
4 117 90
5 96 76
The cost in beakers isn't exact, as it can't be determined precisely when you need 39 turns at 3 beakers per turn - it could be 117-119 with the same result (for example).
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