Kokarev won the U-18 section of the World Youth Chess Championship in 1999 in Oropesa del Mar, Spain.

[1] In 2009, he tied for 1st–8th with Sergey Volkov, Igor Lysyj, Aleksandr Rakhmanov, Valerij Popov, Denis Khismatullin, Dmitry Andreikin and Dmitry Bocharov in the Voronezh Open tournament.

[2] In 2010, he won the Mumbai Mayor's Cup chess tournament[3] and tied for 1st–6th with Maxim Turov, Alexey Dreev, Martyn Kravtsiv, Baskaran Adhiban and Aleksej Aleksandrov in the 2nd Orissa Open tournament in Bhubaneshwar.

[7] Kokarev played for Novosibirsk's team "Siberia" which won both the Russian Team Chess Championship Premiere League[8] and the European Club Cup in 2015.

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