In regard to games it is possible to reduce some cooperative game down to a non-cooperative counterpart allowing for a solution to be found. I think this might be an extendable observation.
For example, thinking about a 9 player poker table, such a game could seemingly be reduced to a heads up counterpart where the hero is playing a game versus an octopus with each tentacle playing a different strategy (the game would be somewhat different, or there would be need for some modification as in the standard perspective the 8 players do not collude).
On another note we could view players that deviate from rational/optimal strategies as being wholly rational if we think of them as having hidden utility functions (or information).
The introduction of money as a transferable utility is said to give rise to the possibility of changing a game from zero sum to non zero sum. Money, in this sense, gives the possibility of part or granular solutions akin to the introduction of a sub game of bargaining. More efficiency and a choice of a higher paying equilibrium can sometimes result.
Cooperative games by definition introduce enforceable contracts.
Contracts themselves can be seen as ranging from reliable to not and/or in relation to money (or payoffs) and the expected stability of it such money over time (ie the duration of the contracts involved).
Here I think we have covered a basic generalization of games that is more general than typically observed.
For example, what is the difference between a single player with a complex utility function and strategy versus a fully functioning coalition (made up of multiple players) with perfectly enforceable contracts that enforce a comparable strategy with equivalent pay-offs?
We could view a non-cooperative game then from a cooperative sense, but with certain restrictions that could be held either through broken communication, differing transferable utility values, or different contractual arrangements.
Poker as an example could be viewed as “Hey let’s get together in a cooperative manner and brute force a solution to poker by trying to beat each other as much as possible.”
It wouldn’t render the game solvable but it opens a lot of objective possibilities for observation that might not be immediately intuitive.