We’re likely entering the end-game scenario for Comcast and Disney’s pursuit of Fox’s assets. However, an obscure U.K. takeover rule called the “chain principle” has altered the bidding dynamic in what’s become a game of three-dimensional chess.

The U.K. has different rules around mergers and acquisitions than the U.S. One of these rules is a lesser-known guideline called the “chain principle.” The idea is that if a target company’s ownership is split, and a would-be acquirer bids on one portion of the target, the implied value of the portion of the company that received the takeover offer must be carried over to fairly value the rest of the company.

It’s sort of like the transitive property of equality — if A=B and B=C then A=C.

In this case, if Comcast tops Disney’s June 20 bid for Fox’s assets, it also affects its other outstanding bid for Sky — now valued at $34 billion. That’s because part of the Fox bundle of assets is a 39 percent stake in Sky. So if Comcast were to increase its bid for Fox, it’s also increasing the value of Sky that Fox owns.

Since Comcast now has the highest bid for Sky, at 14.75 pounds per share, an improved bid for Fox could raise the value of Sky even higher. In some respects, that would mean Comcast is bidding against itself for Sky.

The U.K. takeover panel hasn’t said yet if it will rule that the chain principle applies here, but a decision is expected to come soon.

If Comcast doesn’t bid again for Fox, it’s surrendering in its quest to acquire the other Fox assets, such as Star India, a 30 percent stake in Hulu, Fox’s movie studio and cable channels FX and National Geographic. Both Fox and Comcast plan to sell Fox’s regional sports networks, and Endemol Shine (of which Fox is selling its 50 percent stake) is running its own separate sales process. Fox’s shareholder vote on Disney’s current offer, valued at $71.3 billion at announcement (and higher if the takeover panel assigns a new value to the baked in 39 percent of Sky), will take place on July 27, if Comcast doesn’t rebid.

Even if Comcast feels like it’s better off just bidding for Sky because the value of the other Fox assets are too richly priced, it still may bid again for the entire bundle, CNBC contributor and former TiVo CEO Tom Rogers said on Thursday on “Squawk on the Street.”

“If you’re doing some game theory here, what Comcast should probably want to do if it believes that Disney is going to top any bid it makes for the Fox assets is to bid higher,” Rogers said. “It weakens Disney. It makes it less likely that Disney is going to authorize Fox to go higher in the bidding for the Sky assets.”

And Fox, which is working in concert with Disney, similarly has an incentive to bid again on Sky for two reasons. First, if Disney wants to own 100 percent of Sky, it will have to outbid Comcast. Second, if Disney wants to make sure Comcast only walks away with Sky, pushing the bid higher for the U.K. pay-TV company may be a defensive move to protect the remainder of the Fox assets.

In the end, the more expensive Sky and the Fox assets get, the more likely it is that the two companies will split the assets, rather than strain their balance sheets to afford everything, Rogers said.

However, if Disney does decide it wants it all, the new home base for a bidding war could be around Sky rather than Fox.