Striking is not a game- or is it?

Game theory has been back in my thoughts this week.
Principally I've been looking at whether models of ultimatum and dictator games have a role in decisions take around clinical commissioning shifts.
At a tangent the medical profession has voted to undertake a day of action, which will see many Doctors dealing with only urgent or emergency activities.
In theory they are striking to show that they care about their pensions being changed by the government to give a poorer deal.
However that response is not just a response in the ultimatum game played by the politicians, the one that says "here's our offer, like it or not that's the offer -take it or leave it- your choice". It will be perceived as the first move in a new game played with patients. In the patient game the profession plays the role of dictator, "this is our offer- one day no routine care - no choice,tough luck pal".
There is a reasonable body of research behind game theory and the strategic choices made in the simple Dictator and Ultimatum games. In ultimatum games the offer is usually less "unfair" and more altruistic than when the dictator game is played, most offers see both sides achieve significant benefits. The dictator games are different. When the dictator is protected by anonymity the choices work out to be more extreme.
Almost unwittingly the UKs medics are being manoeuvred into a game they do not want to play, the damage will be significant, the belief that "my GP" has "my best interests" at heart will be demonstrated to be patently untrue, not just for the loss of routine care for that one day, but for the way in which the game has been played with patients.