I am a new owner and trying to rebuild a couple franchises and am running into something I don't understand: How do minor-leaguers accept a higher bid when you can only bid what they are asking for? I understand offering a major-league contract to them or a spring training invite would trump a minor-league deal, but what about higher bids for a minor-league contract?

You cannot add additional salary or bonuses to minor league contract offers.  The only thing you can add, as you've already pointed out, is a ST invite.

Most likely, the deal breaker is probably something no longer in your control, as in the other team you're bidding against has better minor league coaches.  The emails are confusing in the way they're worded because they make it sound like it's about money.  But in those cases, it's really about development and opportunities for advancement.

I understood it as being that the sim evaluated your depth chart and the player would opt in favor of the chance for more playing time.  Hope I didn't just make that up in my mind.

Good point.  That's another possible reason, too.

Cool. Thanks for the input.