Proof of stake requires that you are holding coins, making miners personally invested. If a fork occurs, consensus is driven by the fact that stakeholders would lose value if they allow the fork to continue, so they will form consensus quickly.
When you chose a side of a fork, you risk having chosen the wrong one. So it seems rational not to chose. Let the other miners take the risk. After all, they won't let the currency collapse right?
It seems that the Nash equilibrium for this game will then be that none of the miners take the risk, consensus is lost, and the currency does collapse. Perhaps I'm missing something though.
When you choose the side that everyone else ends up choosing as well, you end up profiting from the block reward and also collecting the transaction fees. If you mined the side that ended up being shorter, then your block rewards are part of a transaction that the network considers to be invalid, as in, it never occurred. So there is incentive to try to figure out which side of a fork is the most beneficial and also which side is going to be preferred by other miners based on their affiliations with the addresses in the transactions for either side of the fork.
Also consider what has been risked - electrical energy, a small amount of bandwidth, and the ever-present risk of hardware failure. The return is in units of a deflationary currency. In practice the number of wasted blocks is quite low since the network ends up being in consensus most of the time. In the past it has been quite profitable to mine using GPUs and FPGAs.
