Ex: when company A partners with company B to create a competition where company B customers can win a trip provided they subscribe to A and B. Who pays for the trip if they're only getting email addresses?
Typically these types of partnerships have detailed contracts that lay our which party is responsible for paying out any kind of competition winnings. There could be all kinds of goods/services trading places between the companies so it isn't as clear as "Company B always pays". You would need to look at the contract between the two companies.
If its Company B's customers that can potentially win the trip, then Company B should pay more of the bill. That being said, who is receiving more value? If Company A is receiving more value by offering a trip to Company B's customers, then Company A should pay more. Another route you could take is with prize insurance. Create a competition where potentially no one wins - Ex. a hole in one during a company golf tournament. You pay a few hundred dollars and potentially someone can win a car. However, I think the answer to this question is based on who is receiving the most value. It doesn't matter if they are just email addresses.
This is a fantastic Marketing Strategy! If done right all parties associated can benefit from it greatly. I have seen this strategy used in several different methods. However, I personally have had the trips donated to me usually by a startup travel agency or an acquaintance that I know is looking to get into the vacation rental business and needs more customers. Would love to speak with you further about other options if you're interested in pursuing this marketing strategy!