Notes on the Comparability of 2 Player Non-cooperative games and 3 Player Cooperative Games

Nash was studying the modeling of 3 person cooperative games using mathematica with the idea that players could give agency to another player thus rendering the game down to a two player non-cooperative scenario.

In his work he explains that because of the complexity of “simple” 3 player cooperative game its not at this time necessary to go beyond and consider 4 or 5 or n person cooperatives games.

I’ve written about this before, that I find this comparable to the 3 body problem which it seems we have also not mastered, as if the moon the sun and the earth are players trying to find an equilibrium with respect to each other.

Nash very loosely refers to the applicability of such equilibrium solutions and game theoretical observations in regard to our world politics.

I’ve also written about this before. We can note if the world had two major uncontestable (but between themselves) superpowers the equilibrium strategies between their negotiations might be simple enough to come to strong agreements (and to use conceptualized meta-game considerations of possible future iterations as a path to a then present time strategy/conclusion).

But of course the world isn’t defined so simply.

Yet if the possibility arises to completely solve 3 player cooperative games by the way of the third competitor giving agency to one of the other 2 players (superpowers) then it’s possible that such observations could become applicable to our real world geo-political/economic reality.

This of course needs to involve truly non-renegable contracts in order that agency can be conceded in a truthworthy manner which is really the complication that makes Nash’s pursuit seem not worthwhile (comparable contracts have been entered into in the past which were then broken with great force such as world wars and jarring economic events etc.)

But if nations and/or superpowers eventually used bitcoin as a settlement medium then I think it is obvious that there could be the basic primitives needed for this sort of scenario described to arise (perhaps we can think of the world as a negotiation between Russia, US, and China but also perhaps there can be two superpowers and the rest of the world can be considered the third player).

Its true the world is far more complex than a model of 3 player cooperative games such as what Nash’s team was modeling however in a world with non-renegeable bitcoin settlement/contracts the significant and comparable factors would be there.

Here I think there is also a derivable observation from Nash’s bargaining problem paper and/or the standard prisoners dilemma which are typically described as having two players. Really depending on our viewpoint, and in considering the “pre-game” bargaining scenario in 3 person cooperative games, these 2 player games could be seen to have 3 players that have already entered into agreements as to what the pay-offs should be depending on the strategies of the players or the choices made etc.

As if the police in a prisoners vs prisoner game are themselves a third player.