Whether to demand withdrawal right now to try to get war is a tough decision. It probably is our best course of action. But - we still have 11 turns left on a peace treaty for which we got two techs. By the letter of the RBCiv rules, that's a phony peace treaty exploit (even if they declare the war). And I think we can still win without resorting to shady tactics like that.
Besides, I'm not too worried about the economic progress of either civ as long as both are at war with each other. We'll continue building, for my turn at least.
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Inherited turn: Since we won't be going to war immediately, I switch Beijing off a rider to a University. Once somebody gets Medicine, we will likely want to research Sanitation ourselves right away. The AIs will probably take a while to get to it; it's a cheap tech (cheapest in the Industrial Age in fact); hospitals will immediately double our military production rate and increase our economy by 50%; and it's also quite possible to trade Sanitation for another tech like Industrialization or at least some cash. But not until someone gets and we somehow acquire Medicine.
Beijing is at 3 turns to university, so I MM it to all the high-commerce tiles.
1305 AD: Shanghai factory -> coal plant.
For the first time I notice that we are in Monarchy - I actually didn't realize we weren't in Republic. Well, revolting now wouldn't make sense, of course.
1310 AD: Beijing university -> colosseum; it will need the extra happiness once a hospital comes or if we lose a luxury colony.
1320 AD: Beijing back on military production, though I'll let it do cavalries every other turn rather than wasting workers and cash to build them every turn.
1325 AD: Shanghai coal plant -> university, same reasoning as Beijing.
1330 AD: Greece has researched a technology before Arabia did - but it's Communism.
And Greece is now in anarchy.
1340 AD: Arabia has also acquired Communism, and also revolted. Both enemies are in Communism.
1350 AD: Nothing else happened.
The units on our western border were there to block any settlers from poaching our Spices. Arabia just settled Sana'a there, so they probably don't need to be there anymore, except for the one way out on the tip (next to the fish) where an AI might settle.
Greece lacks Coal; keep checking him to see if he ever has enough gold/turn to offer to make it worth selling him some.
We can go after Arabia in one more turn after the peace treaty expires, or four turns if we wait for all the payments to expire. (Our reputation betrayal was against Greece; as long as we don't betray Arabia and Arabia is at war with Greece we can deal normally with Arabia.) Or we can go after Greece again; we could've even done that on my turn but I didn't.
Or we can keep trying to build towards hospitals (and maybe Stock Exchanges), although it might be a long while until anyone gets Medicine or Corporation. I don't think we'll reach a winning position against Arabia until artillery, but we can chip away at them in the meantime. (Maybe we should be building cannons now instead of more cavalry, but that's up to the next leader.)
http://www.civfanatics.net/uploads4/lk47-1350ad.zip