Baldwin and friend Spyridon Contogouris claim Costner and business partner Patrick Smith duped them of their shares of an $18 million deal for BP to buy oil-separating centrifuges after the April 2010 oil spill.
Costner's attorney, Wayne Lee, said his client played no role in Baldwin and Contogouris' decision to sell their shares in a company that marketed the centrifuges to the energy company for $1.4 million and $500,000, respectively.
"Kevin Costner is here for one reason and one reason only: He's famous," Lee said in opening statements.
Plaintiffs' attorney James Cobb accused Costner and Smith of spinning a web of lies that cheated his clients out of millions of dollars, telling the eight jurors that the case is about deception "fueled by power and greed."
Baldwin and Contogouris are seeking more than $21 million in damages. Costner and other defendants also are seeking damages in counterclaims.
U.S. District Judge Martin L.C. Feldman told jurors they could not be swayed by the celebrity status of Baldwin and Costner, who sat at opposite ends of the courtroom and didn't interact.
"Celebrity has no place in this courtroom or in any of the issues that need to be resolved," the judge said.
Among Baldwin's roles was caveman Barney Rubble in "The Flintstones: Viva Rock Vegas." Costner's films include the Academy Award-winning "Dances with Wolves," as well as "Bull Durham," ''Field of Dreams," ''No Way Out," ''The Bodyguard," and "JFK," Oliver Stone's conspiracy film about the assassination of President John F. Kennedy.
Lee said Costner, who had lost roughly $20 million in an earlier effort to market the centrifuge technology to the oil and gas industry, decided to lobby BP to use the devices after the oil spill because he wanted to help protect the Gulf Coast from the nation's worst offshore oil spill.
"No good deed goes unpunished," Lee said.
Baldwin and Costner are expected to testify at trial. Baldwin told The Associated Press his attorneys had advised him not to comment.
At the height of BP's efforts to stop the massive flow of oil from its blown-out well, the company ordered 32 of the centrifuges and deployed a few of the machines on a barge in June 2010. BP capped the well the following month and the well was permanently sealed in September 2010.
Baldwin and Contogouris claim they were deliberately excluded from a June 8 meeting between Costner, Smith and BP executive Doug Suttles, who agreed to make an $18 million deposit on a $52 million order for the 32 machines.
As the trial's first witness, Smith said Contogouris was highly involved in the efforts to secure a deal with BP and only has himself to blame for missing the June 8 meeting with Suttles.
"He exited on his own accord, prior to the meeting," Smith said.
"They concealed the fact that BP looked favorably upon funding this," Cobb said.
Cobb said "insult was added to injury" when Costner and Smith used BP's deposit to buy out Baldwin and Contogouris' shares in OTS.
Smith's attorney, Roy Cheatwood, said Baldwin and Contogouris "hedged their bets" and sold their shares before BP committed to the deal.
"They want their cake and they want to eat it, too," Cheatwood said. "They want the money they had and they want the money they chose not to risk."
Pacific West Resources, a company operated by Costner and Smith, also is a defendant in the case.