Why does my dog lie down when another dog comes close?

It looks like he is stalking the other dog, but his ar$e is in the air. Then when the dog comes close enough to sniff he does, then he starts pawing at the other dog if they don't run or try to chase him.Is he just trying to get some play started or is it something i should discourage. If the dog chases him or plays like that he doesn't paw them.He doesn't show his teeth and does wag his tail.

Crouching down - submission stance. With teeth bared - I'm about to attack. Front legs down and bum high - instigating play. And the pawing is similar.Just let your dog interact, watch and learn what the various body language means. But do be careful he doesn't try this on with the 'wrong dog'. Not all dogs want to play.

He is submitting saying he wants no trouble I would say he wants to play butt in the air is a play bow.

sounds like the submissive act of a southern catahoula cur but using it like a bait and lure...hmmm

by the sounds of it, he is asking the other dog to play. does he growl, show his teeth? if he does, then i would suggest discouraging it. does he wag his tail? because this is a friendly sign, which means he wants to play. i would say that he is just trying to play. but still look out for them signs. and then you will be able to tell if he is warning them or asking them to play. hope this helps.

Bum in the air means he's inviting the other dog to sniff him. This is good. It's like holding your hand out for a handshake. By pawing he's trying to initiate play, or possible if his pawing is trying to get his head over the other dog he's trying to assert dominance but not in an aggressive way.

When a dog lies down to another dog he/she is giving a signal that it already is willing to admit that it is offering no threat. Dogs are pack animals and many dogs accept automatically that they are definately not an alpha male and have no intension of trying to be one,thus by laying on the ground it submits immediately to being a follower and not a leader. The pawing is a further signal that it wants regognition that its message has been understood and also accepted.

I asked a question very similar to this a little while ago about my puppy. I was told it's a submissive behaviour because the dogs we meet are older than her and she's putting them above her. I was also told to allow her to do this so they sort out a pecking order. [: