Elsewhere in this blog I extol the virtues of "anchoring" - stating a price early on as a means of setting expectations. This is a good psychological tactic but can be abused, at which point it becomes a "hardball" play.
Highball/lowball is one of the oldest hardball tactics. The American Management Association study of the most common negotiation tactics found that Highball/lowball is actually THE MOST common tactic, with 29% of respondents reporting it.
With Highball/lowball the other party will start the negotiation with a ridiculously high (or ridiculously low) offer, to try to force you to radically drop your resistance points and goals. If you haven’t prepared properly, or you aren’t aware of what is happening, you may be tempted to fall for it. DON'T!
One way to deal with a ridiculously high or ridiculously low offer is to call the other side's bluff - and refuse to continue unless they make a "serious offer". By insisting on a more reasonable opening offer, rather than trying to counteroffer, you force the other side to continue the negotiation on your terms while appearing to be reasonable yourself.
One thing I have often used with a party making a "highball" offer in litigation is a serious REALITY CHECK. It goes something like this: "It's the easiest thing in the world for you to sit there and dream up the wildest number you could possibly hope to get at trial. You know it's ridiculous, and so do I. But in my pocket today I have a cheque book with REAL money in it." You can adapt this to cover commercial situations - for instance, by reminding them what you both know about their competitors' offering. This also acts an an anchor in itself. The other side have "claims" (which are elastic and fungible) - you have something that is real: MONEY.
If the REALITY CHECK doesn't work then you can threaten to walk away - while keeping the door open for future discussion. Calling out their hardball tactic will show that you are familiar with how these things usually happen, and you won’t continue unless they are more reasonable. If it is less obviously a deliberate "highball/lowball", ask them to explain exactly how they got to their number - maybe they have genuinely miscalculated.
Do your research beforehand and know what your best alternatives (BATNA) and resistance points are. If the other party refuses to cooperate, then you should seriously reconsider whether you can conclude a deal with them now