Players who turned down big-money offers to defect to LIV Golf and stuck with the PGA Tour will be given equity shares in the new for-profit conglomerate being formed by the tour's merger with the Saudi Public Investment Fund, PGA Tour policy board member Jimmy Dunne told ESPN Friday.

Dunne is being credited with orchestrating the new deal between the PGA Tour, the DP World Tour and PIF announced Tuesday. Dunne reached out to PIF governor Yasir Al-Rumayyan earlier this year to begin discussions of the agreement that surprised the sports world.

PIF had previously been funding LIV Golf, leading to the schism in the golf world that saw star players like Phil Mickelson, Dustin Johnson and Brooks Koepka leave the PGA Tour behind.

As for star players who declined LIV's offers and stayed, like Jon Rahm of Spain and Hideki Matsuyama of Japan, they will now be compensated for their loyalty.

"The new (company) would grow, and the (current PGA Tour) players would get a piece of equity that would enhance and increase in value as time went on," Dunne told ESPN. "There would have to be some kind of formulaic decision on how to do that. It would be a process to determine what would be a fair mechanism that would be really beneficial to our players."

The players who joined LIV will not be eligible for that equity plan.

In a separate interview, Dunne told Sports Illustrated on Friday that the newly formed, for-profit entity formed by the merger will retain the PGA Tour name and branding. Its current commissioner, Jay Monahan, who is set to become its CEO, will have the power to disband LIV Golf if he wants.

Current LIV Golf CEO Greg Norman reportedly told staff earlier this week that the league is sticking around long-term despite the PGA-PIF agreement, but Norman might be out of a position once LIV is officially under the PGA's purview. Monahan told reporters on a conference call Tuesday that "taking a competitor off the board" was one of the motives for the merger.

As for Saudi Arabia's involvement in the PGA Tour going forward, Dunne claimed the Saudis haven't promised any monetary investment and the agreement was more about the "right of first refusal" to be the tour's investment partner in the future. The PGA Tour will be the controlling partner of any investment, according to the agreement.

Al-Rumayyan, though, will be the chairman of the PGA Tour following the merger.