Don't think about this equilibrium as something "optimal" per se. Think of it as an occurance of strategies in a game where none of the players have a desire to change their strategy given other players strategies. Note well this can be a stupidly large solution concept and needs some refinements.
Pure Nash Equilibria
Mixed Nash Equilbria
Common knowledge is when every one in the games know a peice of knowledge and they know that others know...and they know that the other know etc etc. It sounds crazy but thats what it is.
Payoffs based on their own actions and the actions of others
Knowledge of other players and game
Added Nature here, might be something to it
1) Type of Game, Extensive, Normal Form
2) Number of Players
3) Set of Actions
5) Utility Functions
6) Pay-Off Functions
The matrix style ones. All players move at the same time.
Players move after each other.
Sub-game Perfect Equilibria, Trembling Hand Equilibria, Proper, Evolutionary Stable Equilibrium, Perfect Baysian Equilibria, Cho-Kreps Refinement