I made a short video explaining what nothing at stake means with proof of stake cryptocurrencies as well as what can be done about it and how much it effects the currency as a whole.

https://www.youtube.com/watch?v=pzIl3vmEytY

In this video I discuss what is generally called a short range nothing at stake double spend attempt. Nothing at stake could mean a few other potential issues, but this is the most interesting to study and the one that is potentially feasible in most Proof of stake systems.

thank you to kushti and the consensus research team (http://consensusresearch.org/) for their work on this subject.