I can agree that the negotiations could be framed under "game theory" but I don't see how it equates to the Prisoner's dilemma specifically.
The PD has only three outcomes for each prisoner
1) GO free (if they rat out the other prisoner who stays silent)
2) Short sentence (if they stay silent and the other prisoner stays silent)
3) Mid-term prison sentence (if they stay silent and the other prisoner stays silent)
3) Long term sentance (if they stay silent and the other prisoner rats them out.
What PD demonstrates is that collectively, the prisoners will do the best if they both stay silent. They both get the short sentence. HOWEVER, because each prisoner had to act without know what the other prisoner is doing as an individual it makes to most sense to rat out their partner, because then their worst case scenario is the mid-term sentence and possible to get off scott free. However, BOTH individuals are likely to choose this option and therefore BOTH get the mid-sentence. Thus they are both worse off had they both kept quiet.
The Prisoner's dilemma does not apply to the NBA for a number of reasons.
1) Choices: In the PD both sides face the SAME choices, with the SAME consequences. This is NOT the case with the NBA negotiations. Theoretically it
could be possible to frame the corresponding choices with corresponding outcomes to each side, but I don't think they work with this case. IF you could demonstrate that they do have corresponding choices with corresponding outcomes then I would rethink this point, but I think that it would very difficult without reducing the actions/consequences to such a vague abstraction that it isn't really meaningful.
EDIT: found a scholarly source that does this have quoted below with the prediction it makes
2) Power: in the Prisoner's dilemma BOTH parties have Equal power to make decisions.
3) Symmetry: The Prisoner's dilemma is described in game theory as a symmetrical game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them.
4) Number of times the game is played: In the PD, the game is, and can only be played once. The prisoners can only make 1 choice, aka choose 1 strategy and stick with it. In the NBA each meeting is an individual game; however, both players are aware of the choices/strategies the other players used in the PAST (previous meetings/games) and use that information to make decisions on how they will act in the PRESENT game/meeting.
In my opinion the "game" being played in the NBA negotiations is more like the
Ultimatum Game.
The ultimatum game, like PD the ultimatum game can only be played once.
In terms of trying to reduce the complex negotiation that is the NBA lockout, I think the Ultimatum game is the most accurate, however, it is played multiple times, with the role of the player making the offer switching between the two parties. The outcome of the Ultimatum game would lead to a general 50/50 split of the money. However, the ultimate game doesn't take into account a couple of key information. 1) The others have other costs, which may make them more likely to want more than the 50%. 2) The players are coming out of a
previous agreement wherein they had a 57% of that split. I think that whatever the outcome of the negotiations, they will be within a close enough range of the 50/50 to uphold the results of the ultimatum game. Unfortunately, this doesn't provide us with any new or meaningful insights in to the negotiations.
To get more meaningful insights the best method would to use
Metagame Analysis which has the theoretical framework to analyse and give outcomes for something as complex as the NBA negotiations. However, A LOT of time is needed to satisfy the methodology, and although possible would be very difficult and time consuming for someone without at least an undergrad in math (which I don't have).
Here is a scholarly paper on Professional Sports labour negotiations and game theory
In the paper they do frame the negotiations in the form of the PD
I still think that the Ultimatum game is more reflective game though.
If we combine the outcomes offered by BOTH the prisoner's dilemma and the ultimatum game, we can predict that they will eventually come to a 50/50 split although reaching the point where they are willing to agree on the split will be very difficult to come to, and will be very tenuous (neither side will be willing to meet in the middle for very long).
although these predictions will probably be perceived as having been met once the negotiations are complete (whenever that is), to me they seem like the kind of answers we'd get if asked a psychic. If we had any mathematical model nerds on the site, they could probably give us juicier predictions on what will happen.
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