Idiomatic Expression that basically says "What's bad for you is good for me"

I think "your death, my life" from Latin "mors tua, vita mea" may convey the idea :

• There is a Latin expression that reads "Mors tua vita mea" which is the law of the jungle. This prevails at every level in this fallen world. It seems to be ancient in origin, meaning "Your death, my life" (or: your death (is) my life). Beyond the dramatic tone of the literal sense, this term is used when within a competition, there can be only one winner. It indicates that that failure of one person is a prerequisite for the success of another.

(oldwaldensianpaths.blogspot.it)

We do have an idiom for this, but it's not sure it's an exact match:

One man's loss is another man's gain (Camb)

when someone gets an advantage from someone else's bad luck

You could use this in a situation where you're waiting in line somewhere, and just as the person in front of you gets to the front of the line, they have a problem that requires them to give up their turn.

A somewhat similar idiom:

cut off your nose to spite your face

to hurt yourself in an effort to punish someone else If you stay home because your ex-husband will be at the party, aren't you just cutting off your nose to spite your face?

to do something because you are angry, even if it will cause trouble for you 'The next time he treats me like that, I'm just going to quit my job.' 'Isn't that a bit like cutting off your nose to spite your face?'

To injure oneself in taking revenge against another.

http://idioms.thefreedictionary.com/cut+off+nose+to+spite+face

The important thing that the other answers are missing is that it's a negative sum game, to use game theory terms. If your neighbor loses two cows, and you get one cow, you have still lost a cow.

It's sometimes referred to as winning by losing less:

In January Rout, Hedge Funds ‘Win’ by Losing Less Than Stocks

_Source

You could also call it a tactical victory, by one definition of the phrase. According to Wikipedia:

a victory where the losses of the defeated outweigh those of the victor.

Maybe "one man's trash is another man's treasure"? It feels similar in meaning, although it refers to possessions instead of events.