I've noticed that being the first to buyout someone can be a disadvantage. I've seen several games where two people are the clear leaders, one of them goes to buy out a cheap straggler for the extra claims, but by dropping all of his cash on that he's now left himself open to being bought by the other guy who now effectively bought out two people. You don't really want to buy someone out just for the claims unless your buying the person that is threatening to buy you. and actually I like having 4-5 shares of a company that gets bought out by someone else. I just doubled my money on those and I can immediately turn around and sink that money into the new owners stock.
Yes ... it always just depends, you can actually win as the underdog by employing such tactics, but it would be very hard to generalize. It depends on a lot of factors and every game is different.
In general though it's not wise to buy out a third player that the person who is threatening to buy you out has shares in.
It's also usually not wise to buy other players out of your company if the game has progressed pretty far, but I can't generalize that, there are always exceptions to the rule, for example if the player you are buying out is about to bought out himself. I very often have a solid lead in the game due to a strong economy (always depends on the game and the map, as I said you can't generalize it) - When I am actually struggling I try to buy someone out, When I am clearly leading, I buy out my own shares and then I buy distributed shares among everyone, to make sure noone can "catch up".
It is not always wise to buy out everyone, you dont know the other person's economy by heart, and the numbers don't tell you everything. I have managed to win several games where someone in the lead went on a buyout frenzy, and after he had bought out his 4th person with 6 offworlds launching goods into space, he still managed to get bought out by me with only 2 offworlds running. Those games are rare but they do happen, buyouts are a risk and if someone is threatening to buy you out, you have to think twice where you put your money.
You ALWAYS have to prioritize your buyouts, there are only 2 reasons to buyout another player:
1) Buyout an opponent that is economically strong and threatening to buy you out.
2) To get ahead of the game and get an economical advantage.
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ALWAYS prioritize (1) over (2) no matter what you may think. Even if that person that's threatening to buy you out costs 50% more (600k compared to 400k).
You will never make back those 400k that you spend on the cheaper player in time to save yourself.
Please do keep in mind that I'm trying to hint at some tactics here, it really depends on the game and how it's going. Very often if you are in an offworld race against someone, and there are only 2 of you that are viable winners, it can help to sacrifice your own economical advance to snatch 3 of his shares (without crippling yourself too much of course) - Whichever player has the most shares in the other player's company ends up winning the game - that's usually how it goes.
But then again - you need to know that this only works if his shares are of the same or less value than your own, and that he doesnt have a lot more resources than you do.
What I see so often happening is that when I start to buy someone out with their stock value being at 10 and mine at 15, they start buying 5 of my shares, instead of buying their own shares and then they get bought out. Unless you have enough money to complete a full buyout against a player of a higher stock value, invest the money in your own shares to save yourself, as every share you buy in your own company is worth twice as much (in terms of survivability).