Bhim may be a different story. For him a challenge by Duryodhana may produce a better result. Remember, Krishna, Buddha or Ram cannot be produced by the method of training or competition. They are unique flowers. Patanjali and Einstein also are in similar boat.
Competition can produce average, the superior is out of the reach of competition.
He feels and teaches others to think to produce their own best rather than compete with others. Why be limited by the limitations of others. Excel with yourself. This in many terms is similar to doing karma according to your swadharma.