Not sure why you were downvoted.
I nice worked for a Big 5 company. I'm not aware of Machiavellian efforts to destroy competitors; they just bought them.
I've worked for an international software company with ~1,500 staff. I do not think our management were inclined to collaborate with their competitors unneccessarily; they had a fiduciary duty to their shareholders.
I've worked for two small-town website developers, with say 10 staff. There's four or five competitors in this town. My management were happy to collaborate with competitors to stage conferences; but I know in both cases they wanted to crush them.
None of these jobs was in SV, or even in the US.
I note the story about IBM's threats (above); so my limited view is that aggressive behaviour between companies occurs across the range of scale.
Incidentally: it doesn't make you seem weak and defenceless that you seek a collaborator in fighting a patent troll. The trolls are backed by venture capital; you are a sole trader. That you are considering defying them is courageous.