Arbitration/subrogation determined I was not at fault for the accident- how do I get my rental paid for?

I was hit by a GEICO policyholder- they refused liability, but subrogation determined he was 100% at fault and I received my deductible back. I didn't have rental car insurance, GEICO initially said they were paying for my rental car then refused, and now they won't reimburse me even after the subrogation determination. 29 days of rental car usage at $18.74 per day- $673.34, How do I sue for this to be reimbursed? Do I sue the driver or the insurance company?