Sure, I'll play Game #2. I'll even play it repeatedly, with a stopping criterion based on my utility of money.

If my utility of money is approximately linear for at least an order of magnitude or so beyond $100 (which it is), the most likely outcome is that I lose all of my initial $100 stake according to a biased random walk on log(pot). However, the game would be very much net positive in expected utility since an exit via the stopping condition wins so much more. It's a lottery biased in my favour, where I get to choose the odds of winning to some extent, but the payout increases better than linear in those odds.

I would prefer to repeatedly play Game #1, or better yet a Game #1.5 where I get to choose how much to bet, but if Game #2 was the only option then I'd take it.

This is fairly well-trodden ground, but I'll respond regardless.

There is important information missing.  I presume these are both once-in-a-lifetime game offers, but it still matters what ELSE one might do with a bankroll and the time spent playing these games.  Game 1 is a no-brainer unless you absolutely need that marginal $40 for something immediately.  Game 2 is "play until your time is more valuable elsewhere".  Depending on rounding, there may be a lower-bound where it's no longer positive EV as well, but for most, it'll be a waste of time to keep playing before that happens.

Game #3 (the opponent decides when to stop, not you) depends on real-world considerations - there's no such thing as an infinite bankroll, nor infinite time to play.  What happens when the amounts get ludicrous?  If he can keep playing until everyone's dead and nobody can collect/pay anyway, then certainly just walk away.  If there's a reasonable maximum value (and timeframe) they'd have to pay out rather than continuing, then play.

The rest are just variations making the same mistake (assumption of infinity).  And the attempt to link to investment "strategy" is just silly.