Arjun prevailed over Abdusattorov 1.5-0.5 while Praggnanandhaa lost an intense battle 3-4 against Caruana.
Having lost three and drawn three coming into the third and final day of rapid, Praggnanadhaa lost to Lenier Dominguez of the US in the seventh round.
Nakamura, who started off as the favourite in the blitz section, is in sixth spot on 13.5 points, ahead of tour leader and compatriot Fabiano Caruana who has 13 points.
R Praggnanandhaa missed out twice on cashing in on winning positions, ending up at the bottom of the table
Indian Grandmaster Arjun Erigaisi opened his campaign with four victories and a solitary defeat in the World Rapid Chess Championship and was tied fifth, even as defending champion Magnus Carlsen endured a frustrating day, managing to log just one victory in New York.
With Georgia likely to post a victory against overnight leader Kazakhstan, it seemed that the Indian eves were likely to regain the top position and become the firm favourites for the gold medal again.
World champion Viswanathan Anand played out another draw, this time with Cuban Lenier Dominguez, but other results of the day helped him go joint-third after tenth round in the Magistral Ciudad de Linares chess tournament.
World champion Viswanathan Anand was held by Teimour Radjabov in the eighth round of the Magistral Ciudad De Linares chess tournament. With six rounds to go in the super Grandmasters event, leader Alexander Grischuk has 5.5 points and the nearest contenders are Vassily Ivanchuk and Levon Aronian, both of whom have 4.5 points each. Anand is joint fourth spot on four points with Magnus Carlsen.
World champion Viswanathan Anand played out a hard-fought draw with Grandmaster Lenier Dominguez of Cuba in the third round of the 22nd Ciudad de Leon chess tournament in Linares on Sunday. Taking his tally to 1.5 points out of a possible three, the Indian ace remains in the joint third spot in the eight-player double round-robin tournament.
The Indian world junior champion emerged joint-winner in the International invitational tournament in Bermuda.
The Indian ace beat GM Lenier Dominguez of Cuba in the penultimate round of the Bermuda invitational chess tournament to move to second place.
P Harikrishna settled for a draw against top seed Alexey Dreev of Russia but managed to grab the second spot
The world junior champion finished sixth following a draw with Lenier Dominguez of Cuba in the ninth and final round of the Dos Hermanas International Chess tournament.
Former World champion Viswanathan Anand suffered a disappointing final round loss against Sergey Karjakin of Russia to finish joint eighth in the St Louis Rapid Chess tournament in St Louis, on Thursday.
Garry Kasparov, arguably the greatest player ever, returns to competitive chess after 12 years.
Former world champion Viswanathan Anand had another disappointing final day as the Indian finished on ninth spot in the St. Louis Rapid and Blitz Chess tournament, a part of the Grand Chess tour.
Former World champion Viswanathan Anand had another bad outing, drawing seven and losing two games, to remain on joint eighth place after the end of nine rounds of blitz in the St. Louis Rapid and blitz chess tournament in St. Louis, United States.
A summary of sports events and sports persons, who made news on Tuesday
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