The rewards during this cooperation phase (fees and new coins) will be fairly distributed among the winners of the previous competition phase. Fairly should be interpreted as proportional. That means that a mining pool that solved 7% of the blocks during the competition phase will get 7% of the total proceedings from every block mined during the competition phase.
Congrats, you've just reinvented essentially Byzcoin, which is incentives incompatible:
https://bitcointalk.org/index.php?topic=1319681.msg16861492#msg16861492https://github.com/cosmos/cosmos/issues/46#issuecomment-266235696Who will invent the next NAOD?
NAOD = nonsense algorithm of the day which repeats mistakes already in the prior art, because the author is too uninformed to cite the prior art.