One activity can equally be done by Division A or Division B of a firm but, for historical reasons, Division A has control of it right now.  This gives the managers of Division A lots of power to hire and they like having a little empire.  But the CEO comes up with a plan: Since both divisions are in theory up to the job, have them compete for the activity.

The best way to do this is pretty obvious: If Division A screws up, give the job to Division B.  But of Division A does a good job let them keep it.  This gives Division A good incentives to work hard to do a good job.

In practice it is hard to measure the quality of output so it is hard to implement this simple scheme.  Quality is evaluated by subjective judgements and rhetorical arguments. Perversely, the better the job Division A is doing, the more incentive Division B has to try to steal the job.  This is because a job well done generates lots of slots.  If Division A is doing a bad job, the activity does not look worth stealing.

So, in practice, having the divisions compete for the activity can lead to destruction of incentives.  Better to give one division the property right over the activity and intervene only when outcomes are objectively poor.

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