It assumes that all employees are informed about other employees playing a quit game. From a management perspective, it may be good strategy to make the counter

It assumes that all employees are informed about other employees playing a quit game. From a management perspective, it may be good strategy to make the counter offer, if you could ensure that it is kept quiet from office gossip. Also, an individual employee has no incentive to broadcast the fact that he is using the threat of quitting, and is likely to play into that stratey if he receives what he wants in pay/status/hours etc.