In a situation where an employee that announces their intent to leave A,
then remains because they were offered terms that matched or exceeded
their offer from B, two interpersonal outcomes are typical. In the
first, A's management views the employee as a more valuable individual.
Apart from the increased money, the individual feels more appreciated
and everyone is happy. Unfortunately, it's been my experience that more
typically A's management feel cornered into matching B's offer; and from
that point on no longer completely trust the employee.