HOUSTON — Picture a three-year-old tug of war waged across the globe that leaves both sides wobbly and scarred but unmoved. That’s one way of looking at the high-stakes competition between the world’s big oil exporters and the companies drilling in American shale fields.

The struggle for dominance of the 97-million-barrel-a-day global market has left a scorecard that few in the oil patch could have anticipated three years ago, when oil sold for over $100 a barrel — more than twice the current price, which is near 12-month lows. With the onset of the summer driving season, oil and gasoline prices should be rising, but they have fallen over the last two weeks as inventories of crude and refined products remain stubbornly high in the United States and abroad.

On one side of the rope is the Organization of the Petroleum Exporting Countries, the Saudi-led group whose strategy for retaining market dominance has twirled from one failed tactic to another as it struggles to conquer a glut that will almost surely suppress prices for at least another year.

And on the other side are the companies still working at a frenzied pace to tap shale reserves in the United States, especially across Texas. They have survived the cartel’s attempts to kill off shale production, but they are limping from the depressed crude prices that make eking out a profit a daily struggle.

At least 123 of the companies operating in North America have filed for bankruptcy since early 2015, and the survivors, like Exxon Mobil and Chevron, have watched their share prices slump well below bull market averages as they borrow to keep up their dividends. More than 150,000 oil workers lost their jobs in the United States alone, although the job market is beginning to recover.

“For both sides, there has been one twist in the road after another,” said Daniel Yergin, the energy historian and vice chairman of IHS Markit, an energy research consultancy. For prices to rise again, “inventories have to be seen as coming down, and there needs to be a tempering in the growth of U.S. shale production,” he said. “Those are the two things that are defining the market right now.”

But neither is happening.

This week oil traders were shaken by a report by the International Energy Agency that global supplies rose by 585,000 barrels a day in May as both OPEC countries and non-OPEC countries increased production. Oil stocks for the 35 industrialized economies, the agency noted, are not only well above the historical average but higher than when OPEC decided late last year to cut output.

United States oil production, which averaged 8.9 million barrels a day in 2016, will rise to 9.3 million barrels a day this year, according to the Energy Department. The department is projecting production of 10 million barrels a day in 2018, exceeding the record set in 1970. Last week domestic crude inventories eased a bit, but gasoline stockpiles rose by 2.1 million barrels.

OPEC set the latest market cycle in motion in late 2014, when the Saudis and their allies decided to swing cartel policy in an unexpected direction. Instead of cutting production to support prices, as it had done so often in the past, OPEC decided to let market forces loose and then even raised production.

The new tack helped stabilize the market for a time, raising the oil price, which had dropped below $30 a barrel in early 2016, to over $50 a barrel during much of the first half of 2017. At that point many oil companies operating in the United States raised production and locked in higher sale prices with hedges.

But OPEC’s cuts were partly a mirage. Its production actually rose by 290,000 barrels a day in May, to the highest level of the year, because Libya and Nigeria were exempted from the cuts and were gushing crude onto world markets.

Political instability could throttle production from either country at any moment, but both continue to surprise the markets with their robust exports.

The low oil and gasoline prices are nice for consumers, but they also hurt the competitiveness of cleaner electric cars. They could also damage the prospects for an initial public offering by the state-owned oil company Saudi Aramco — a move central to King Salman’s efforts to remake the economy.

But another twist may lie ahead in the battle for markets. Lower prices could force companies to slash production again. Already, some are cutting back on exploration and new projects in fields where it is expensive to operate, like the Canadian oil sands.

“It remains to be seen if drilling can continue at the same pace in a sub-$50 environment once price hedges expire,” Mr. Jafar said, referring to the American shale producers. “But if it does, I believe OPEC producers will have no choice but to revert to preservation of market share once again, which could see prices nose-dive. And the cycle will continue.”