Is there a game theory solution for this scenario?

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Consider a finite bunch of publishers each of whom has put some secret amount of money in a pot to acquire a piece of info. The person who submits the

  1. complete info to the pot
  2. first

wins all the money in the pot

  1. if there is at least 1 runner up.

The aim of the game is to incentivize complete publication as fast as possible. Is there a game theoretic approach already available that models this scenario?

Terminology

By submission we mean that the person sends the complete info to the pot. Submissions are private.

By publication we mean that a publisher makes its piece of info public to all others.

End point: The pot waits for at least 2 submissions and makes the info public.

A runner up is the second publisher who submitted the complete info.

e.g. If there were only two people and 3 wasn't applicable, no one would ever publish their piece of info as the non publisher wins. (In fact the last person not publishing would always win). With 3., the last publisher publishes post submission.

Is there a way to ensure everybody does publish?

Feel free to extend the problem.