https://en.m.wikipedia.org/wiki/V._R._Parton#Synchronistic_Chess
For each turn players decide their moves, write them down secretly, then disclose them. They adjust the position accordingly, using the following rules of resolution when needed:
If moves were to the same square, then White captures Black if the square is on Black's half of the board; Black captures White if the square is on White's half.
If moves were reciprocal captures, then
both pieces are removed from the board.
If one player moved to a square the opponent's piece occupied, but that piece moved away in the turn, it is considered captured and removed from the board if it is of lower rank (K > Q > R > B > N > P). If it is the same or higher rank, then both moves stand.