It is the theoretical question (no real bitcoin award) from the game theory.

Suppose, that somebody grants valuable amount of BTC (let's say 10BTC). The private key is published online: for example, a separate thread is created (here on bitcointlalk) with the announcement to publish private key on certain date and time. While the private key is published, everybody (who read the topic) could release the funds. However, we know that replace-by-fee (RBF) transactions are possible. So, if the user 1 makes a spending 9.99BTC with 0.01BTC comission, so another one could make RBF transaction with 9.5BTC and 0.5BTC, and miners will confirm the transaaction with higher fee. The 3d user could make 9BTC spending with 1BTC transaction and so on... The users also could negotiate online making pools, promissing equal shares to each other. However they also could break such negotiations to maximize personal income.

The questions are:
[1] How much will be spent from such 10BTC address and how much will be the transaction fee to miner?
[2] Suppose, that only 4 online anonymous to each other users have the access to disclosed private key. These users also could negotiate online. How much will be spent from 10BTC address and how much will be the transaction fee in this case? 4 users can easily negotiate (let's say to receive 2.49BTC each, transaction fee 0.04BTC), but everybody will still have temptation to replace the transaction with higher fee and higher personal reward (9BTC spending with 1BTC transaction fee for example, where 9BTC is much more than 2.49BTC)