Libya is hosting the World Chess Championships, in the latest plank of Colonel Muammar Gaddafi's strategy to end years of international isolation.
The Libyan leader is a calculating player
This is the first time the event has been held in Africa and Libya is putting up $1.5m in prize money.
But a row over the participation of Israeli players marred the start to the competition on Saturday.
And most of the world's top players are boycotting the tournament in a dispute over the event's organisation.
In response to a row over visas, the World Chess Federation (Fide) said visas would be issued to Israeli players on arrival.
Israeli coaches, however, were barred from entering the country, and the Israeli chess body is now considering suing the Libyans and Fide for compensation.
Libya failed to win the 2010 World Cup bid
"I am somewhat surprised that you don't see the importance of having the World Chess Championship in Libya, during the time when the country is opening up to the international community," Fide president Kirsan Ilymzhinov said in reaction to criticism.
Libya once hosted military bases for Palestinian groups and does not recognise Israeli passports.
Last year, it publicly ditched their weapons of mass destruction programme, and declared a stockpile of chemical weapons to UN inspectors.
Only two of the world's top 10 players have gone to Libya, because they are angry that the world's highest rated player Gary Kasparov was allowed to play the winner without going through the qualifying rounds, reports AP news agency.
Libya also bid to host the 2010 football World Cup but South Africa was chosen instead.
The knockout championship of the world's top players concludes on 13 July.