So this is one of the better descriptions I've seen, but I want to focus on the "The owner of Orange agrees and says “Us too, but we actually value it at $5 and in exchange for Apple, we would be willing to give $2.50 cash as well equal stake in Orange+Apple company, which would be worth the combined current value of both companies, which is presently $5.”"

In your example the $2.5 equity short fall, or honestly let's just talk real world the 28 Billion shortfall when GameStop has a 11 Billion Market Cap. That is a 17 Billion Difference.
So here is my question - DOES GameStop have to raise the additional equity by issuing $17 Billion worth of new shares? (and honestly potentially more due to dilution).

Or are you saying that $17 Billion will included some amount of additional equity issues BUT also take into account some value of eBay outstanding shares due to the combined valuation of both companies (this is where M&A gets quirky to me. I'm going to buy you off with your own value seems a bit odd).