If the width property is set to 100%, the video player will be responsive and scale up and down:
video {
width: 100%;
height: auto;
}
Notice that in the example above, the video player can be scaled up to be larger than its original size. A better solution, in many cases, will be to use the max-width property instead.
If the max-width property is set to 100%, the video player will scale down if it has to, but never scale up to be larger than its original size:
video {
max-width: 100%;
height: auto;
}