Making an Elevator

I’ve been trying to make an elevator that moves only downward to a platform and stops. But my script doesn’t seem to notice the player. Can you tell me what’s wrong please?

Here’s the script:

using UnityEngine;
using System.Collections;

public class FallingPlatform : MonoBehaviour {
	bool isFalling = false;
	float downSpeed = 1;
	void OnTriggerEnter(Collider collider)
	{
		if (collider.gameObject.name == "player") 
		{
			isFalling = true;
		}
	}

	void Update()
	{
		if (isFalling)
		{
			downSpeed += Time.deltaTime/10;
			transform.position = new Vector3 (transform.position.x,
				transform.position.y-downSpeed,
				transform.position.z);
		}
	}
}

@Chell_Aperture did you make a tag called player and assigned it to the player?