If several people update the same file on different devices, Resilio Sync will synchronize the changes in chronological order, starting with the change that was made first and up to the most recent one. Note, however, that Sync propagates the latest file that comes online. Therefore, if a peer modifies a file in an offline state and then goes back online, their file version will have a priority over those versions which were proposed by other peers in an online state (even if chronologically those versions were submitted at a later time).
Here are some examples.
Case 1:
Suppose there are 3 peers online. Peer 1 updates a file in a synced folder at 10:00, then Peer 2 makes some changes to the file at 10:10, and Peer 3 offers some updates at 10:20. In this case, Sync will be syncing all the changes based on the time when the file was modified: Peer1 > Peer2 > Peer3.
Case 2:
Suppose there are two peers. Peer 1 goes offline and modifies a file in a synced folder at 10:00. Peer 2, who stays online, makes some changes to that file at 10:10. When the first peer goes back online, their changes (even though they were made earlier) will have a priority, and will be synced to Peer 2. Thus, the updates made by the second peer will be overwritten. All overwritten file versions will be placed in the archive.
To access archive, click Folder options > Open archive...