Icons: System States

I had a very interesting discussion regarding Aristotlean Drama, Linear Programming and Transactional Analysis today and it lead me to reevaluate my own thoughts on these concepts.

First I reevaluated my thoughts on States:

states-aristotle-drama

states-linear-program

states-transact-analysis

Aristotlean Drama is simple because it only involves the state of one character following a linear path.

However, when you begin to think about the outcomes for two characters the dynamic becomes tabular which brings us to game theory and the famous prisoner’s dilemma and game theory payoff matrixes:

prisoner-aristotle-diad

prisoner-linear-diad

prisoner-transact-diad

However, it immediately becomes apparent that the Prisoner’s Dilemma does not account for all of the States.

prisoner-aristotle-triad

prisoner-linear-triad

prisoner-transact-triad

Here we have the States of Transactional Analysis, however this state model is not complete either.

prisoner-aristotle-pentad

prisoner-linear-pentad

prisoner-transact-pentad

Even with a pentad the States are incomplete.  This is where my epiphany came in.  There has to be a begin state and an end state.

prisoner-aristotle-heptad

prisoner-linear-heptad

prisoner-transact-heptad

Now with a heptad, we have all seven States and a complete tabular model.

However, we are learning tabular models are not adequate.  We are learning network models are necessary.  And network models require an alternate portrayal.

prisioner-aristotle-hex

prisoner-linear-hex

prisoner-transact-hex

Here we have a network presentation of the seven States.  And each of these States have seven states of their own.  There is no magic here.  The correlation to the week I do not think is coincidental, but cultural, however I do not think that astronomical phenomena have any causation.

prisoner-score-hex

Related Link:

Social Psychology: Escaping the Prisoner’s Dilemma

For the past several decades the Prisoners’ Dilemma has been a dominant frame in Game Theory. It’s quadrant model has crossed the boundaries of many disciplines especially political science, economics, business, biology, computer science and philosophy. There are also the games Stag Hunt, Chicken and Hawk-Dove which are 2×2 games. My argument in this post will be that the Prisoners’ Dilemma is not adequately representative of reality.

merrillflood.jpg melvindresher.jpg

The Prisoner’s Dilemma was originally framed by Merrill Flood and Melvin Dresher while working on game theory at RAND in 1950 which Rand pursued because of possible applications to global nuclear strategy.
albertwtucker.jpg

Albert W. Tucker formalized the game with prison sentence payoffs and gave it the “Prisoners’ Dilemma” name (Poundstone, 1992).

The game has two prisoners who cannot communicate and each has only two moves:

  1. to conceal their guilt or
  2. reveal their guilt

They are aware of the potential outcomes of their actions as follows:

pdmatrix01.jpg

The canonical payoff matrix for the game is represented as follows:

pdmatrix025.jpg
In “win-lose” terminology represents the game in the following manner:

pdmatrix03.jpg

The flaw I see in the Prisoners’ Dilemma is that it only provides the following payoffs:

  1. Win-Win (Collaboration)
  2. Win Much-Lose Much (Exploitation)
  3. Lose Much-Win Much (Exploitation)
  4. Lose-Lose (Altercation)

It does not provide for Win-Lose or Lose-Win (Distribution). The absence of distribution may be suitable for Mutual Assured Destruction (MAD) games, but not for most other human transactions. Consequently the Prisoners’ Dilemma can be presented as follows:

pdmatrix10.jpg

Now, I am going to take a different tack with the Prisoner’s Dilemma.

ericberne1

I am going to view it from the perspective of Stephen B. Karpman’s Drama Triangle, a concept derived from Eric Berne’s Transactional Analysis. However, I am going to adhere to game theory’s premise that the players are rational.

Stephen categorized interpersonal transactions into three roles:

  1. Persecutor
  2. Rescuer
  3. Victim

In the Prisoners’ Dilemma there are only the Rescuer and the Persecutor:

pdmatrix09.jpg

In what I will call the Transaction Triangle game there are three roles and thus three moves:

pdmatrix11.jpg

In “win-lose” terminology the Transaction Triangle is as follows:

pdmatrix07.jpg

And the canonical payoff matrix is as follows:

pdmatrix12.jpg

As you can see, distribution is incorporated into the model to provide for most human transactions while still preserving the key components of the Prisoners’ Dilemma. I also concluded that the lose-lose payoff of the Ultimatum Game was suitable to provide for no transaction taking place. It is time to abandon the 2×2 mindset of mutual assured destruction and adopt a more human and realistic 3×3 game frame.

Further Reading: