Played a few games, and they all seem to indicate that there is indeed a bug with the research focus.
In the manual, it says you can set the research focus for your realm (not your demesne), but what happens is that all AI-controlled provinces always have their research focus set on BOW, FARM, and NOBLE, regardless of the research focus you have set in the TECHNOLOGY tab (as indicated by the FOCUS BONUS number shown when you put the pointer over the military/economic/cultural advances icons in each province). This doesn't just apply to your vassals, but even to enemy AI provinces (of course you shouldn't be able to choose their focus, but that's not the point).
However, the problem doesn't just end with you not being able to dictate what your vassals research.
This also results in AI research essentially being crippled, since there is severe AHEAD PENALTY (since the AI researches the same tech over and over), which I am assuming is the penalty you suffer if your tech level is ahead of the general historic date when such a technology existed. Seeing that AHEAD PENALTY is nothing to laugh at, it puts the AI at a severe disadvantage compared to the player. (Of course there is the possibility that the AI research could be operating on a totally different system, despite what the actual number say to the player). It also severely takes away the AI's competitive edge due to the AI's infantry (not archers) falling behind those of the player, the enemy not being able to increase the tax they get from their city/church holdings through relevant research, and so on.
I haven't been able to check whether the research focus for AI-controlled provinces changes whenever the research in a particular area is raised by 1 level, but seeing how all AI-provinces have the same FOCUS, I don't think it does.
In the manual, it says you can set the research focus for your realm (not your demesne), but what happens is that all AI-controlled provinces always have their research focus set on BOW, FARM, and NOBLE, regardless of the research focus you have set in the TECHNOLOGY tab (as indicated by the FOCUS BONUS number shown when you put the pointer over the military/economic/cultural advances icons in each province). This doesn't just apply to your vassals, but even to enemy AI provinces (of course you shouldn't be able to choose their focus, but that's not the point).
However, the problem doesn't just end with you not being able to dictate what your vassals research.
This also results in AI research essentially being crippled, since there is severe AHEAD PENALTY (since the AI researches the same tech over and over), which I am assuming is the penalty you suffer if your tech level is ahead of the general historic date when such a technology existed. Seeing that AHEAD PENALTY is nothing to laugh at, it puts the AI at a severe disadvantage compared to the player. (Of course there is the possibility that the AI research could be operating on a totally different system, despite what the actual number say to the player). It also severely takes away the AI's competitive edge due to the AI's infantry (not archers) falling behind those of the player, the enemy not being able to increase the tax they get from their city/church holdings through relevant research, and so on.
I haven't been able to check whether the research focus for AI-controlled provinces changes whenever the research in a particular area is raised by 1 level, but seeing how all AI-provinces have the same FOCUS, I don't think it does.
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