Sabernomics discusses the Yankees/A-Rod negotiations from a game theory perspective. He argues against Jeffrey Gordon's point that the Yankees refusal to negotiate is not credible:

A-Rod won't wear the pinstripes again. I am certain that the Yankee's are out of the bidding, even though the Yankees might still value his services more than any team in baseball. What is at stake here is not a single player's contract, but the organization's long-run credibility at keeping its word. If the Yankees cave, the repercussions will echo into the future. Why would any player ever not opt out of his deal in the future if he knows the Yankees will give in? Not following up on your threats is bad for your reputation as a tough guy.

Exactly right.