https://www.googleapis.com/drive/v2/files/{FILE_ID}/permissions?key={YOUR_API_KEY}
{
    "role": "writer",
    "type": "anyone",
    "withLink": true
}

https://www.googleapis.com/drive/v2/files/{FILE_ID}/permissions?key={YOUR_API_KEY}
{
    "role": "writer",
    "type": "user",
    "value": "******@outlook.com"
}