When a basketball player dribbles a ball, it falls to the floor and bounces up. Is a force required to make it bounce? Why? If a force is needed, what is the agent involved?

Energy is the one that is stored in the ball when it drops. Just before it hits the ground, the energy depends on the mass of the ball and its velocity. When the ball hits, it is compressed and the energy is stored in the compression of the air in the ball and the elasticity of the material that the ball is made from. Some is also converted to heat. The stored energy in the ball causes a force to make the ball back into a round shape and this force presses against the propels and floor the ball back up. The small amount lost as heat is the reason that the ball bounces up with less energy than when it hit.