Difficult negotiations are sometimes described as multidimensional chess. The cliché is more apt than usual as American and Iranian envoys meet in Switzerland, while Israel and Hizbullah, their respective allies, continue attacking each other. That could undermine talks that were not going to be easy at the best of times (which these are not).

And Chinese AI is a bit behind the American kind, but generally thought much cheaper. But our analysis, including of a much-hyped new Chinese model, shows that China may be both more capable and less competitive on cost than usually thought.

What to expect in the week ahead:

▸ Sir Keir Starmer is reportedly set to announce his departure from office, perhaps as soon as Monday. Britain’s prime minister has always said that he would fight a leadership challenge, but cabinet ministers are now said to have told him he faces being forced out if he does not set a timetable to leave on his own. Monday will also see Andy Burnham, Greater Manchester’s former mayor, sworn in as an MP, following an impressive by-election victory in Makerfield last week. Mr Burnham is the clear favourite to become Britain’s next prime minister, but—in taking the top job—stands to inherit a ledger of thorny issues from Sir Keir.

▸ New York’s Democratic primary election is set to take place on Tuesday. It will be the next big test of the party’s ideological direction, with candidates who are not quite far enough left struggling against insurgent challengers. Anger at President Donald Trump and Israel has been boiling over in Democratic primaries across the country. In New York they are given greater heat by the new leftist mayor, Zohran Mamdani.

▸ America will publish important inflation data on Thursday. The personal-consumption-expenditures price index, the Federal Reserve’s preferred measure, rose to 3.8% in April, spurred by higher oil prices and a strengthening labour market. Kevin Warsh, the new Fed chairman, remains under pressure by Donald Trump to lower rates, despite above-target inflation. Mr Warsh and his colleagues kept rates unchanged at his first policy meeting last week, but nine out of 18 Fed officials forecast at least one increase this year.