IN their book, “Getting to Yes,” Roger Fisher and William Ury introduce what may be the most important concept in the theory of negotiations: the best alternative to a negotiated agreement, or Batna. Knowing your true Batna — and your adversary’s — is critical in bargaining. A vivid example from the entertainment world illustrates the concept and offers some useful hints about how the current fiscal negotiations in Washington are likely to unfold.

The Warner Brothers 1999 hit comedy “Analyze This” portrays a mob boss (Robert De Niro) and his psychiatrist (Billy Crystal), who share a passion for the recordings of Tony Bennett. With the film almost completed — and with Mr. Bennett already an integral part of the plot — the studio finally got around to approaching the crooner with an offer of $15,000 to sing “I’ve Got the World on a String” in the movie’s closing scene. But as Danny Bennett, the singer’s son and business manager, later explained, the executives made a fatal mistake by not scheduling this conversation sooner: “Hey, they shot the whole film around Tony being the end gag and they’re offering me $15,000?”

Had studio officials made their offer at the outset, they would have had much more leverage. If the Bennetts demanded an unreasonable sum, the filmmakers could have rewritten the script and used some other singer. At the 11th hour, however, Warner Brothers’ best alternative to a negotiated agreement was to spend hundreds of thousands of dollars reshooting the film. In the end, the studio paid Tony Bennett $200,000 for a brief cameo appearance.

A similar logic is shaping the current negotiations between President Obama and Congressional Republicans. The Republicans want to keep everyone’s tax rates the same while raising revenue by closing tax loopholes yet unspecified. The president, for his part, wants to restore the 39.6 percent top tax rate for families earning more than $250,000, while maintaining current rates for everyone else. But with the Bush tax cuts scheduled to expire at year’s end, the Republicans face a hurdle similar to the one that confronted Warner Brothers.