It's definitely possible using the Drive Activity API. You can use the Quickstart for Google Apps Script to view all the activity of an item (file or folder) or done by a User. In this case I modified the Quickstart to show the Permissions changes of a given Drive Id.
function listDriveActivity() {
var request = {
itemName: "items/1bFQvSJ8pMdss4jInrrg7bxdae3dKgu-tJqC1A2TktMs", //Id of the file
pageSize: 10};
var response = DriveActivity.Activity.query(request);
var activities = response.activities;
if (activities && activities.length > 0) {
Logger.log('Recent activity:');
for (var i = 0; i < activities.length; i++) {
var activity = activities[i];
var time = getTimeInfo(activity);
var action = getActionInfo(activity.primaryActionDetail);
var actors = activity.actors.map(getActorInfo);
var targets = activity.targets.map(getTargetInfo);
if (action == "permissionChange"){ //Only show permissionChange activity
Logger.log(
'%s: %s, %s, %s', time, truncated(actors), action,
truncated(targets));
}
}
} else {
Logger.log('No activity.');
}
}
/** Returns a string representation of the first elements in a list. */
function truncated(array, opt_limit) {
var limit = opt_limit || 2;
var contents = array.slice(0, limit).join(', ');
var more = array.length > limit ? ', ...' : '';
return '[' + contents + more + ']';
}
/** Returns the name of a set property in an object, or else "unknown". */
function getOneOf(object) {
for (var key in object) {
return key;
}
return 'unknown';
}
/** Returns a time associated with an activity. */
function getTimeInfo(activity) {
if ('timestamp' in activity) {
return activity.timestamp;
}
if ('timeRange' in activity) {
return activity.timeRange.endTime;
}
return 'unknown';
}
/** Returns the type of action. */
function getActionInfo(actionDetail) {
return getOneOf(actionDetail);
}
/** Returns user information, or the type of user if not a known user. */
function getUserInfo(user) {
if ('knownUser' in user) {
var knownUser = user.knownUser;
var isMe = knownUser.isCurrentUser || false;
return isMe ? 'people/me' : knownUser.personName;
}
return getOneOf(user);
}
/** Returns actor information, or the type of actor if not a user. */
function getActorInfo(actor) {
if ('user' in actor) {
return getUserInfo(actor.user)
}
return getOneOf(actor);
}
/** Returns the type of a target and an associated title. */
function getTargetInfo(target) {
if ('driveItem' in target) {
var title = target.driveItem.title || 'unknown';
return 'driveItem:"' + title + '"';
}
if ('drive' in target) {
var title = target.drive.title || 'unknown';
return 'drive:"' + title + '"';
}
if ('fileComment' in target) {
var parent = target.fileComment.parent || {};
var title = parent.title || 'unknown';
return 'fileComment:"' + title + '"';
}
return getOneOf(target) + ':unknown';
}
Remember to enable the Drive Activity API in Resources > Advanced Google Services
In my example this returns the logs:
You can also look deeper into the Permissions by using the permissionChange Parameters in the query.