The reason the price goes down is because then you are not the only one offering it anymore.
A tech is valued double in trade if there is only one person offering it. Other civs may have the tech, but if they have no contact with the one you are offering it to, for them you are still the only one offering, so you get double value.
Thus, you could check if there are civ's that do not have contact with eachother and trade it to those first.
-Check if there is any civ who offers tech(s), the other civs do not yet have. These you can trade on to the other civ's after trading them for yourself. This is the most important thing when deciding who to trade to.
-Check if there are 2 civs you can rip off as explained above.
-Check what civ has the most expensive tech to offer. the cheaper ones you most likely can also get when the price is halved, the more expensive ones maybe not (that espescially includes techs on wich the AI has monopoly, but also simply their relative value)
By selling again the techs you get from them in trade, you should be able to get all available techs in one turn after being the first to discover a new tech, even if you are several techs behind. It is important you do this all in 1 turn, else they will trade amongst eachother.
When in the end, you sold a tech to multiple civ's but not all, do not hesitate to sell it to those last ones as well, even if it will be for a low price. If you dont do it, another AI will do it. They will get it within few turns anyway.
Try getting gold per turn payments from them. I like gold per turns a lot more than just gold, because it also slows them down in their research, even if they have 1000's in the bank. If you manage to get gold per turn from most civs, not only do you have a nice income for yourself, you are also slowing down the general tech pace, enlarging your chances of getting more first researches.
If yuo now get some gold per turn payments with your tradings and still an AI is the first to research another tech, it is a very good option to buy that tech from him for gold per turn. You can then sell it to all other civs for gold per turn.
This is THE strat that enables people to win deity / sid games. It requires you to check the diplomacy every turn though. if you wait 1 or 2 turns after an AI has gotten a tech, chances he sold it to all other AI's grow from possible to most likely. (thus disabling you to sell it to them)
Sometimes though, it is wise to wait a bit until he sold it to only 1 other AI for then he wont be the only one offering it to you, thus halving the cost for you. This is best done if you know he is at war with many civ's and thus you can be sure that while you wait for him to sell it, he wont sell it to everyone immeadiately.
Finally, never give in to AI's trade initiativs. If you do trade in their turn, they can pass the tech you pay them on to every other civ in their turn as well. So only trade during your turn.
