The decision follows a separate ruling today, in which sports retailer JJB Sports was told that it had failed in its attempts to quash a similar price-fixing fine of£6.7 million.
All parties said they were disappointed by the rulings, which upheld earlier decisions by the Office of Fair Trading and Competition Appeal Tribunal.
The Court of Appeal refused all three parties permission to appeal to the House of Lords, but they are said to be considering whether to petition the Lords directly.
Argos, which was fined£15 million for fixing the prices of Hasbro toys and games, said it had made a provision of£16 million in its end of year accounts in March last year.
JJB, which was fined for fixing the prices of Umbro shirts, raised the amount it had set aside to cover the fine from£2 million to£3.88 million when it posted its interim results yesterday.