In nature, the cooperation is often accompanied by the competition with group members when they divide the cooperatively produced rewards through competition. In such a case, the evolution of cooperation and competition influence each other, but previous theoretical studies mostly focused on either cooperation or competition. In this study, we consider a two-player game where two individuals are cooperatively produced rewards following the continuous snowdrift game, and the produced reward is divided within them following the tug-of-war game. By using this game, we investigated the coevolutionary dynamics of two continuous traits, i.e., investments in cooperation and competition. In the results of the numerical simulations, we found that the within-group competition promotes the evolutionary branching and therefore polymorphism in cooperation level and competition level occur. In the polymorphic population, the cooperation levels are always positively correlated with the competition levels among strains, and therefore the cooperator often exploit the reward of cooperation from cheating individuals. We also found that the mean cooperation level within the population is promoted by the existence of the competition. These results show the cooperation accompanied by the competition causes qualitatively different evolutionary outcomes from evolution in the only-cooperation or only-competition.