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This tutorial will tell you how to share PSN games with other people, bought or free (I think this won't work with HOME though).

For the "sender":

1. Purchase and download a game from the PlayStation Store
2. Go to account management for the account and delete the billing information from your personal information if the PS3 saved your credit card info
3. Change your password temporarily for the share
4. Give login info (email address and password) to the receiver
5. When the share is completed, change the password

For the "receiver":

1. In the PS3 XMB menu, add a new user account on your PS3 and sign in to it
2. Select the network on the XMB and create an existing PlayStation Network account
3. Use the login information given from the "sender" to create the existing account
4. Login into the account
5. Enter into the PlayStation store
6. Click on "Download List" on the upper right near the person's UserID and select the game you wish to download and hit download
7. After game is downloaded, notify the "sender" that the download is complete so they can change the password to the account
8. Enjoy!