I currently work for a big 4 firm right now, and have been dealing with some restatements as a result of stock comp expense. This is what I understand about the accounting for options:
When options are issued, they typically have a 4 year vesting period. For each year end reporting period, a company would recognize the portion of the option that vests (i.e. 25% of the option). This is an expense that hits the P&L. So you are correct that net income goes down (which in turn is retained earning). This would cause the equity portion of the accounting equation to go down (Assets = Liabilities + Stockholders Equity).
I think the second half is where you might be getting confused. When expense is debited for say $100 for stock comp expense, an offsetting $100 is credited to additional paid in capital. This would cause stockholders equity to increase. So the two sides of the equation balance (Equity goes down for the expense, and then goes back up for the APIC). There is no affect on Assets on liabilities.
I think the above is fairly accurate, however I have only been working in accounting for 1 1/2 years now, and this is still a relatively new topic for me.