There is something verging on insanity about the deep and justified pessimism that surrounds Gaza cease-fire talks that started Thursday, because every state that’s even tangentially involved has more to gain than lose from a deal.

That’s always been true of the mediators. For the U.S. there are only downsides to a conflict that risks dragging it into a much more destructive regional war; it has already eroded America’s international image and influence and become a source of division at home. Egypt needs traffic and revenue back to normal through the Suez Canal, as well as stability on Gaza’s frontier with its own volatile Sinai region. Qatar needs to demonstrate the value of its long-standing policy of hosting Hamas, a terrorist organization capable of the atrocities of Oct. 7.

Other regional powers need an agreement, too. The Gulf States are all strained by the tension between their populations’ outrage over the plight of Palestinians and their own strategic plans to build an economic and security arrangement with the U.S. and Israel that would isolate their major concern: Iran. Lebanon, meanwhile, risks being turned into a wasteland if a resolution can’t be found in Gaza, because Hezbollah has said it won’t stop striking Israel until that happens, and Israel has said it will escalate unless it does.