Coherent Cooperative Games and Understanding

Getting on the same page…

“Coherent Cooperative Games and Understanding”. Image by ChatGPT-4o and Victor Morgante.

We naturally understand that understanding is when we have the same mental model as someone else.

This naturally lends to Coherent Cooperative Games and as I describe them:

“If you play, there is only one type of play or move which is that on each move you play the other player wins. The rules of the game are open and coherently known to each player. Play tokens are defined by the rules and may be the rules themselves.”

How would each player know that the other player is winning in their subjective view?

Coherent Cooperative Games (CCGs) allow for a Differential Interpretation Game (DIG) where differences are discussed, worked through, debated etc in order to arrive at a CCG, a new-CCG or disengagement altogether: More [here]

The Coherent Cooperative Game Transition Diagram. Image by author.

But what is in-sync between players in order for there to be a Coherent Cooperative Game?

Mutual understanding.

However to break out of the word-play cycle, if we consider concepts within the mind as points of structure, cojoined to form larger concepts, we can then transition mindset over to formal logic, which was designed in the first place in order to train and structure thinking as to be logical, which we would wish a Coherent Coopertive Game to be.

That being the case, we can test for isomorphism, or a homomorphism between structures between people’s minds (or the inner workings of an AI) using Ehrenfeucht Fraisse Games (EF Games).

Now, for those who consider EF Games only under Finite Model Theory (FMT), we lift the finite domain restriction, or consider that FMT operating over finite domains an arbitrary restriction on a model introduced by humans and where any First-Order Logic (FOL) may be considered a Higher-Order Logic (HOL); and if we take a highly unconventional approach, but that of having been studied and applied, we reverse it and consider that an arbitrary but practical Higher-Order Logic may be expressed as a First-Order Logic and we can equally arbitrarily restrict the model to the finite.

I.e. We leave open EF Games to be played over points of structure asserted by either FOL or a HOL and the practical reasoning over a broad domain of a human or AI mind.

In that case, with either player playing Spoiler or Duplicator in an EF Game, we have both players winning having found an isomorphism between disparate structures, or a homomorphism between the structures as a sub-set of a larger structure, being the structure of a sub-CCG or more colloquially “It’s all fun and games until it’s not”.

Isomorphic Structure found between disparate structures. Image by author.

I consider such “Getting on the Same Page” resolution to a Coherent Cooperative Game, for instance, in my article on debating new legislation (a DIG) to arrive at a new set of laws from which a Coherent Cooperative Game may be played in Formalism for a Game-Theoretic Approach to Law.

And that is how I picture Coherent Cooperative Games (and their associated DIGs) arriving at mutual understanding.

Get Victor Morgante’s stories in your inbox

Join Medium for free to get updates from this writer.

Remember me for faster sign in

Thank you for reading. As time permits, I will write more on Coherent Cooperative Games and their application.

— -
More in this series here on Medium:

1. Coherent Cooperative Games — As I describe them;
2. The Genesis of Coherent Cooperative Games;
3. Coherent Cooperative Games — Described;
4. Coherent Cooperative Games and the Law;
5. Formal Logic — And Coherent Cooperative Games;

….and…

1. All of Logic is a Game;
2. The Atoms of Knowledge;
3. What is Formal Logic;
4. Applied Use of Ehrenfeucht Fraisse Games;
5. What is a Graph Database;

…and…

1. The Atoms of Knowledge;
2. The Richmond Architecture;

…and where it all started:

1. Morphing Conceptual Models.

===============End===============