Coherent Cooperative Games — Described

Unification of Game Theory, Communication/Information Theory and Formal Logic

“The Work Desk”, Royalty free image by DALL-E 3 and Victor Morgante

I describe Coherent Cooperative Games (CCG) as games where:

“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.”

That formal logic is best described as a Coherent Cooperative Game stems from the position that formal logic nothing without one or more interpreters, each a player, with payoff being an interpretation and formation of models/structures that makes sense to each individual player.

When one or more players share the same interpretation, a Coherent Cooperative Game over a finite set of exchanges of theorems of the formal theory under investigation, as a communication of the information of the theorems and the data they operate over, is established.

Which is all to say that formal logic is about communication/information theory and game theory, and where game theory is not an adjunct of formal logic but superior to formal logic and envelopes it. Communication is a form of formal logic, and is a game. Games are a form of communication.

Differential interpretations are possible, and we call these a DIG, Differential Interpretation Game; by default a non-cooperative game.

With this framework, which I describe in my white-paper on the same, we have the foundations of describing formal logic as being predominantly with the intent of engaging in a Coherent Cooperative Game, or investigation/playing of a DIG.

Differential interpretations may be non-intentional or intentional. A Coherent Cooperative Game then, a Nash Equilibrium under which plays can be made ad infinitum even as a subset of differential interpretations (a homomorphism of interpretations) but where the desired state a Coherent Cooperative Game where all players play by the same interpretation and on each move played such that the other player win.

My initial article on Coherent Cooperative Games describes this as the most boring game on Earth, but where the harmony, synergy and cooperation of a CCG outweighs defection to a DIG, or where a DIG may lead to a new stable Nash Equilibrium state and a new Coherent Cooperative Game.

If we step out of formal logic, and focus on the game of logic and where logic a metaphor for the thinking process of individual players, then we can get a better overview of Coherent Cooperative Games.

Coherent Cooperative Games are visible in politics, law, interpersonal relationships, data mapping, paradigm shifts, marketing, information sharing, child rearing, permeation of religious beliefs and ideals, education, assertive behaviour, journalism, driving cars on roads, international business and economics. All describable as games, all having Nash Equilibria, but where the desire if for a Coherent Cooperative Game and if we consider common good the outcome, and defection via a DIG either subversive, strategic, manipulative, aggressive (as in a takeover) or in general non-cooperative until some new Coherent Cooperative Game is established as a form of order focused on each player winning.

A Coherent Cooperative Game differs from subjective perceptions of winning and losing, and focuses on communication of what is perceived as winning by each player in order to establish the CCG such that each player may play such that the other players win.

Road rules fall under this category. Perceived as universally accepted within a Country or State, the notion of driving on the right side of the road is a subjective strategy of each player such that all other players win. By virtue of every player adopting this strategy, one’s own safety is assured.

I.e. We do not play a CCG because we have to, but because we want to for the benefit of each player. That Nash Equilibria are formed is by virtue of a CCG, and a Nash Equilibrium is not the game itself. A Nash Equilibrium describes the state of play, rather than a holistic view of a strategy that leads to a Nash Equilibrium that may benefit each player.

In my main article on Coherent Cooperative Games, I clearly outline that such things as unpayable debt arrangements are not a Coherent Cooperative Game. Just because someone works to pay off an unpayable debt, for instance, does not mean they enjoy it, that the situation is right, or that the lender cannot afford debt forgiveness, for instance.

Coherent Cooperative Games are not a call for altruism, but realism, in respect that where it can be afforded, it makes sense to show the equivalence of altruistic notions with accompanying action, as it leads to there being a win-win, and better still when each player considers it a win.

That is, if I repay by subsequent transactions an unpayable debt, and enjoy it, then we get close to a Coherent Cooperative Game. More pointedly, if I do not enjoy it then we are definitely not playing a Coherent Cooperative Game.

I believe this adequately describes Coherent Cooperative Games and as I describe them. Peace and harmony in symmetry a desired outcome, sometimes with a DIG that is managed respectfully, rebelliously, chaotically, strategically or by result of miscommunication or misadventure, when a new Coherent Cooperative Game is established, by way of new Nash Equilibrium/s, such peace and harmony exist with a balance of cooperation. I.e. Agreeing to disagree lacks the cooperation of a CCG, and peace will come when, if and only when, the fighting is right.

Thank you for reading. As time permits, I will write more on Coherent Cooperative Games, game theory, information/communication theory, formal logic and the sometime wonder of playing such that the other player wins.

=====Further Reading=====

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. What is Formal Logic;
3. Applied Use of Ehrenfeucht Fraisse Games;
4. What is a Graph Database;

…and…

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

…and where it all started:

1. Morphing Conceptual Models.

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