If you do something for the sake of something you do it for that purpose or out of consideration for a specific person. To do something for someone's sake or for your own sake means to do something for someone else's advantage or with a specific motive in mind. The expression for God's sake or for Pete's sake are exclamations of anger or surprise and are much more informal and used in social contexts.

1. If we say, for the sake of argument, that the competition lowers their prices, how are we going to compete?
2. Let's assume, for the sake of argument, that there is a tax introduced on sugar...what products are we working on that won't be affected?
3. I think we should bring up the topic for the sake of discussion. We need to speak about it.
4. For the sake of expediency, we should increase the workforce so that we meet the deadline.

1. For your own sake, I think you need to quit that job and find something else.
2. For the sake of my sanity, I send the children to my mothers for the weekend.
3. For Maria's sake, we took a long walk around the lake. She had never been there before.