“I have a couple of counterparts who are bent on getting whatever they want regardless of what I do. I find myself giving in most of the time or ending up in deadlocks in those instances I don’t.  It can’t be like this each time. What else can I do? Edwin- Supplier-side Manager
Hi Edwin, I will respond to your query, whilst largely in the context of the contents of your accompanying letter, yet taking some liberties to generalize some points to enable our other readers to benefit from my broader analysis and recommendations.
First of all let us try to understand the various types of negotiation hardliners according to motivation.

1.      The Blind Mimic Hardliner – This fellow either watched too many movies or merely emulates role models usually out of context.
2.      The Issue-fixation-skewed Hardliner – Rationally-anchored, this negotiator is on a self-justified, bulldozing crusade to secure what his                  side needs, undaunted and unmindful of the detrimental consequences his demands will have on his counterpart’s camp.
3.      The Emotional-myopia-skewed Hardliner – Like having a last song syndrome (LSS), this person is overwhelmingly gripped by the                        emotional components of the negotiation issue, thereby blindsiding options and tunnel-visioning to just a single selfish goal                                      which unfortunately is inimical to the counterpart negotiator’s camp when acquiesced to.
4.      The Balanced Hardliner – Albeit the label sounds like an oxymoron, ‘balanced’ here refers to an equal weight being placed by this                          fellow on both the rational issues and emotional components, fortifying reason with emotional resolve.

With the exception of the blind mimic and the balanced hardliner, the two other types of hardliners respectively require either reason-anchored or emotionally-skewed plays to dial them down to cooperation. This means neutralizing emotional negativity or trumping logical assumptions or painting grim consequences, should the present trench warfare attitude not be replaced with more dynamic concession exchanges. For balanced hardliners, doing both will be necessary. As for blind mimics, simply guiding them out via their own backdoor exits will allow them to change their positions without losing face. These can be accomplished by providing external reasons or assumption changes to induce abandonment of position, again without loss of face.
The depth by which hardliners dig into their trenches, also vary relative to the rational and emotional components’ motivational weights, the climate changes of the negotiation atmosphere, the negotiating styles of their counterparts vis-à-vis relationship between the parties.
In dealing with hardliners, directly counterattacking their issues or emotions single dimensionally is the least effective. This is bargaining instead of negotiating, quite likely to end up in a deadlock. The usual reaction of hardliners is to dig in deeper when cornered!
Strategic Approach
From a strategic perspective, prior to facing hardliners, reinforce existing power whenever possible, particularly when coming from weakness. It is preferable to enter a gunfight with more than a knife in your hand, unless you are some Machete or Ip Man reincarnate!  You can augment your leverage, by introducing other power sources, beefing up strength of existing ones or replacing your walk away option with something more attractive, just in case things go south. Another perspective is to strategically ask yourself, can you bombard the hardliner’s fortification prior to your face-to-face meeting, utilizing allied marionettes your puppet strings have access to? If affirmative, do so preferably with plausible deniability, feigning non-relation to your cause. 
Tactical Approach
Tactically disarming the hardliner’s sources of leverage early in the game will funnel your discussion to a more cooperative type instead of combative negotiation. Consciously adjusting negotiating styles to be non-confrontational, yet never submissive nor hesitant, would work wonders as well.
Alternatively, various flanking moves can be used to induce them to soften up or even abandon their well-defended positions. One type of flanking move is to provide a powerfully relevant counter issue that puts pressure in another front making them lose their full attention on their stronghold. If a multi-variable trade-off can be considered, then the grip has become effectively loosened. Alternatively, if your side has more time to spare, time-induced pressure can also work to your advantage. This is best executed by playing with negotiation atmosphere variables that will slow down the process. After all, time will always outlast power.
Rowen Untivero is a Partner and Chief Sales Strategist of Mansmith and Fielders, Inc., the country’s leading marketing, sales, strategy and innovation training company.  Rowen developed the world’s first Nego-mathematics, strategic Nego-mapping, and 3D Influencing Language Wheel. He has been injecting much practicable science into negotiations, selling and management for more than a quarter of a century. Please send your questions, comments or feedback to mentors@mansmith.net. You can alsovisit www.mansmith.net.