Protracted conflicts typically end in one of two ways: Either the party with overwhelming force subjugates the other and declares a complete victory, or the two sides get tired of fighting and make a deal.

In Hong Kong — now in its sixth month of an increasingly violent, seemingly intractable conflict — China’s communist rulers and their handpicked chief executive, Carrie Lam, seem intent on achieving a total victory over a leaderless, loosely organized, youth-driven protest movement that has paralyzed the city and plunged the economy into recession. The protesters “will never win,” Lam has vowed, and it’s “wishful thinking” to believe that the government will ever yield. And there’s no doubt China has the overwhelming power in this dispute, as well as the will to dominate.

But Beijing is not going to get its way.

Already, it has tried. Hong Kong police have fired more than 8,000 rounds of tear gas, thousands of rubber bullets and hundreds of beanbag rounds, and have made more than 4,000 arrests. Three people have been shot with bullets. The authorities have used a new law to ban wearing masks in public and a colonial-era statute to charge protesters with the crime of “rioting,” which can carry a 10-year prison term. A curfew appears to be under consideration. Universities (including the University of Hong Kong, where I teach) have suspended classes for the remainder of this year. Police in full riot gear have raided university campuses, commercial buildings, even churches.

None of it has worked. Black-clad, ninja-like protesters roam the streets undeterred, and the protests enjoy broad public support, including among white-collar professionals. Brutal police tactics have elicited only heightened violence from the protesters: What started as brick throwing toward police has descended into gasoline bomb attacks, arson, vandalism and gruesome assaults, including protesters setting a man on fire. A 70-year-old man died after being hit in the head by a flying brick. Force has been met with force in an escalating cycle of violence.

It hasn’t worked because the protest is popular and the protesters are committed. No new draconian laws, no new tactics, no increase in tear gas and live rounds, no heightened arrests will push or frighten Hong Kong’s determined protesters off the streets. Short of an outright slaughter — which, in an era of smartphones and surveillance cameras, seems not to interest Beijing — force is not enough. China may not want to admit it, but the only solution to this crisis is a political one. Communist Party leaders will have to do something that to them is an anathema: They will have to make concessions.

The broad contours of a common-sense way to end the crisis are quite clear. Like the Arab-Israeli two-state solution, or a power-sharing agreement in Afghanistan between the U.S.-backed Kabul government and the Taliban, everyone knows what the final outcome will need to look like. The warring parties are merely battling over the steps to get there.

In Hong Kong, based on the declared goals of the protest movement, any resolution has to begin with the ouster of Lam as chief executive. Her ill-conceived, widely despised idea to allow people arrested in Hong Kong (which has a respected legal system) to be extradited to face trial in mainland China (where torture and forced confessions are common, and where prosecutors enjoy a 99 percent conviction rate) triggered the current crisis. She clung stubbornly to this bill even after 1 million Hongkongers, or 1 out of every 8 people here, marched peacefully in protest. She is by far the least popular chief executive since the territory reverted to Chinese sovereignty in 1997.

Lam’s cabinet will have to go, too. They allowed her to push the extradition bill despite widespread opposition because they are radically out of touch with average Hongkongers. They are so tied to the elite, and to Beijing, that they either ignored or underestimated the widespread anger on the streets.

Hong Kong’s underlying problem — and the root of this crisis — is the absence of politics. Where else could a leader see a quarter of the population marching in the streets and still forge ahead? It’s because here, the top official is not accountable to the people but is handpicked by a Communist Party dictatorship in a capital 1,200 miles away. She answers to Beijing, not to constituents.

For that reason, reform will need to include an expansion of the democratic franchise to allow all the seats in the local legislature (instead of half, as they are now) to be elected by popular vote, and universal suffrage for the election of the city’s chief executive. The Communist Party in Beijing will always reserve the right to vet the candidates. But people in Hong Kong deserve a say. And given the past sorry chiefs picked by Beijing — two who didn’t complete a second term, one jailed for corruption and now Lam — allowing the people to decide is a certain improvement.

Protesters will also insist on some form of accountability for what happened: an independent commission to investigate unlawful police behavior since the start of the protests. Officers, operating with Beijing’s backing, have indiscriminately lobbed thousands of canisters of tear gas at largely peaceful demonstrators, have used pepper spray, beanbags and rubber bullets at close range, and have been recorded abusing subdued and handcuffed protesters.

Journalists trying to cover the demonstrations have also been targeted, seemingly with impunity. Police now use flashing strobe lights affixed to their helmets to prevent the filming of arrests on public streets. Several reporters have been pepper-sprayed and tear-gassed despite wearing yellow vests and helmets marked “PRESS.” Some have been severely injured, including a reporter from Indonesia who was shot in the face with a police projectile and blinded in one eye. Lam says the existing police watchdog body can probe any accusations of excessive force, but officials who know its workings say its resources are inadequate for the job.

Finally, protesters want amnesty for those arrested during the demonstrations, and they want rioting charges dropped. Those demands could be answered by a commission tasked broadly to look into violence on all sides, and by holding for trial only those who injured others. A model might be the South African Truth and Reconciliation Commission, set up after apartheid, which granted amnesty to those who voluntarily came forward and testified truthfully.

At the moment, Beijing’s leaders and their representatives in Hong Kong have stood firmly behind the police and urged even tougher action to quell the protests — while never specifically rejecting the call for an independent commission. The Financial Times recently reported that Beijing has already decided to remove Lam sometime next year. Lam herself was recorded saying she would have quit at the start of the unrest “if I [had] a choice,” but she later denied she intended to resign.

So far, the conflict here has looked like the collision of an unstoppable force and an immovable object. Neither side wants to give up. For the protesters, it would mean surrendering their cherished freedoms and becoming completely subjugated to Beijing, becoming just another mainland Chinese city; for Beijing, it would mean showing signs of weakness, bowing to demands from the street and potentially triggering what the authoritarian leaders fear most — the protest contagion spilling over the border to neighboring Guangzhou and elsewhere in China.

But the costs of persisting — terrible pictures of violence beamed across the world, mass arrests, the long-term alienation of a population whose submission China needs — will, sooner or later, prove too high. Beijing’s going to have to make a deal.

Twitter: @keithrichburg