DOHA, Qatar — Victoria Beckham came from London. Diane von Furstenberg and Alexander Wang from New York. Pierpaolo Piccioli of Valentino flew in from Rome, while Olivier Rousteing of Balmain and Giambattista Valli came from Paris. So did Carla Bruni, with her husband, former President Nicolas Sarkozy of France, firmly in tow.

They were part of a pantheon of the biggest names in fashion that descended upon Doha last week, to mix with Qatari dignitaries and socialites and act as judges for the inaugural Fashion Trust Arabia prize. Twenty-four hours earlier, the same group — alongside the artist Jeff Koons and the soccer manager José Mourinho, as well as celebrities including Johnny Depp and Sonam Kapoor — had attended a star-spangled opening event for the new National Museum of Qatar, featuring Bedouin dancers, musicians, singers and flag-wielding horseback riders.

Few, if any, of the boldface names at these gatherings had ever been to Doha before . Their en masse arrival, however, on the invitation of the ruling Al-Thani family, was an unmistakable demonstration of the unlikely influence of Qatar, a tiny Gulf state where vast natural gas resources were discovered almost 60 years ago, helping to make it the most wealthy country per capita in the world.

It was also the latest move in a cultural and architectural arms race raging in the Gulf. Rival nations that stem from the same Bedouin roots, share the same religion and eat the same food compete to establish distinctive national identities and status amid political volatility, colliding cultures and intense economic upheaval.