This week has already been tabbed as the beginning of Robert Dudley's reign as BP's (NYSE: BP) CEO. Tony Hayward's three-year stint was cut short by the company's involvement in the worst environmental disaster in the history of the United States and by Hayward's own inability to avoid stuffing his foot -- and sometimes both feet -- in his mouth.

Beyond that, however, there's some potential that Dudley could head up the last executive administration in the company's long history. U.S. political events could dramatically shape BP's future. How? Simply by determining whether the big British company is permitted to go on plying its trade in our country.

From my current perspective, however, I'd be surprised by a movement from Washington, D.C., that would strip BP of its right to drill for and produce oil and gas here. But anything is possible, especially with Gulf Coast folks progressively getting their dander up about BP's slower-than-desired pace of reparations to spill-affected Gulf residents.

Beyond that, however, there remains at least something of a possibility that BP's Big Oil peers could make a run at the company, especially given a continuation of the substantial reduction in its share price that followed the April 20 disaster aboard Transocean's (NYSE: RIG) Deepwater Horizon rig. Halliburton (NYSE: HAL) was also embroiled in the controversy thanks to a cementing job that may or may not have contributed to an explosion and fire, along with 11 deaths and a three-month oil spill that befouled the Gulf of Mexico and the shore areas of the five states that border it.

I've discussed with my Foolish friends, even while the Gulf spill was still gushing, the notion that BP, with its newly anemic share price, could be gobbled up by the likes of ExxonMobil (NYSE: XOM) or Royal Dutch Shell (NYSE: RDS-A). In fact, I might even toss in a dark-horse run by Chevron (NYSE: CVX), whose own market capitalization now outranks BP's and has a net cash position.

So the wild and wacky world of BP continues. I must state that Robert Dudley -- the first American to run the venerable British company -- has demonstrated his ability to survive amid difficult political and geopolitical circumstances. For instance, Fools interested in energy likely recall his tough times as CEO of Russia's TNK-BP partnership, a successful but contentious joint venture among a group of Russian billionaires and BP.

Before affairs at the partnership settled down, Mr. Dudley held things together, until both parties finally made nice. I'll not be surprised if he's able to accomplish a similar revival at BP. The result could be pleasant profits for Fools willing to stick their necks out at today's BP prices.  

Chevron is a Motley Fool Income Investor pick. The Fool owns shares of ExxonMobil. Try any of our Foolish newsletter services free for 30 days.

Fool contributor David Lee Smith doesn't own shares in any of the companies named above. True to its name, The Motley Fool is made up of a motley assortment of writers and analysts, each with a unique perspective; sometimes we agree, sometimes we disagree, but we all believe in the power of learning from each other through our Foolish community. The Motley Fool has a disclosure policy.