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:

Systema: Whyever? Part 2

270px-extensive_form_game_1.jpg

Part 1 is here.

strategy (n)

4. a plan, method, or series of maneuvers or stratagems for obtaining a specific goal or result: a strategy for getting ahead in the world.

goal (n)

1.the result or achievement toward which effort is directed; aim; end.

rule (n)

1. a principle or regulation governing conduct, action, procedure, arrangement, etc.: the rules of chess.

An extensive form game is a specification of a game in game theory. This form represents the game as a tree. Each node (called a decision node) represents every possible state of play of the game as it is played. Play begins at a unique initial node, and flows through the tree along a path determined by the players until a terminal node is reached, where play ends and payoffs are assigned to all players. Each non-terminal node belongs to a player; that player chooses among the possible moves at that node, each possible move is an edge leading from that node to another node.

It should be noted that even in a game with a finite number of moves (steps) there are generally countless strategies (paths).

Looking at the Extensive Form diagram above and considering the definitions, we can see that the game above has two players: 1 and 2. The numbers by every non-terminal node indicate to which player that decision node belongs. The numbers by every terminal node represent the payoffs to the players (e.g. 2,1 represents a payoff of 2 to player 1 and a payoff of 1 to player 2). The labels by every edge of the graph are the name of the action that that edge represents.

I would like to play with the terminology. I would call the nodes “goals”, I would call the edges “rules” and the paths I would call “strategies”. Goals are actually states of the system and the rules are actually processes. Thinking about it this way makes me think of information architecture and website architecture. Browsing and navigation in this case becomes a one player strategy where the website provides the goals and rule set. However, the design process of the system is to determine the goal set and rule set of the player and provide a “natural” or even more optimal set of strategies for the user to follow.

Part 3 is here.

Systema: Whyever? Part 1

270px-extensive_form_game_1.jpg

Over the past few weeks I have been reflecting on the concept of a Business Motivation Model and have thought about it in the context of physics as “cause”. The Business Rules Group attempted to create a Business Motivation Model, but I came to the conclusion they have failed. When they should have been attempting to create a notational system, they instead came up with a generalized business model.

The purpose of the “Why” focus in the Zachman Framework and correspondingly the Six Hats, Six Coats Framework, is to gauge the order of the system. The Green Hat row and Green Coat Column describe how legalistic the system is–how many causes a system contains.

The best way to think about the causality of a system is not business rules, but game theory. In particular, causality as a three dimensional network relating strategies. A good Business Motivation Model notation would allow the modeler to represent the strategies of all parties, how they interact and the expected outcomes. The Extensive Form Game notation is a good start but I think with some work I could come up with something better.

Part 2 here.

Related Posts:

Systema: Seven Hats, Seven Links