Kaï was called up to New Caledonia's squad for the 2011 Pacific Games. He was the tournament's top scorer with ten goals. Half of Kaï's goal tally for the tournament came in one match, the 9–0 win over Guam on 30 August 2011.[4] He scored all ten of his goals in the group stage before also featuring in the semi-final win over Tahiti and the 2–0 victory over the Solomon Islands in the final.
On 1 June 2012, Kaï scored a hat-trick in New Caledonia's opening game at the 2012 OFC Nations Cup, a 5–2 victory over Vanuatu.[5] He featured in both of New Caledonia's other group stage fixtures but was used sparingly in each game, being substituted at half-time in the 4–3 defeat to Tahiti on 3 June and being introduced from the bench in the second half against Samoa in a 9–0 win on 5 June.[6][7]
On 8 June, he scored New Caledonia's first goal in a 2–0 win over New Zealand in the semi-final, helping his country to the second Nations Cup final in their history.[8] Kaï played the entirety of the final against Tahiti on 10 June but was unable to prevent a 1–0 loss as New Caledonia finished as runners-up.[9] With four goals, Kaï was the tournament's joint-third top-scorer, tied with Benjamin Totori of the Solomon Islands and Tahiti's Jonathan and Alvin Tehau.[10]
Speaking shortly after winning the award, Kaï admitted he was surprised to have beaten off such fierce competition to win the title, saying "To be honest, I couldn't believe [I had won] – it was a real surprise when it was announced. It was only afterwards that I realised what [an] honour it is to have been elected ahead of professional footballers from New Zealand, and I am very proud to have followed in the footsteps of Christian Karembeu...this trophy is also good for New Caledonia football because it shows we have talented players. I would like to thank the football family in my country because without them I could not have reached this level."[14]
In December 2012, Kaï was named New Caledonia's joint Player of the Year along with Patrick Wajoka in the inaugural Football Oscars; both attained 22.38% of the vote in national newspaper Les Nouvelles Calédoniennes.[15] Kaï was also included in the New Caledonian Football Federation's "Team of the Year".[16]
International goals
Scores and results list New Caledonia's goal tally first.[17]