developed by john nash, and having applicability within his game theory, is the 'nash equilibrium.' it is defined by a set conditions that players in a game must meet in order to achieve a maximum beneficial payoff as prescribed by the game. when the nash equilibrium conditions are met, utility, expression, or stability may be reached.
a. The players all will do their utmost to maximize their expected payoff as described by the game.
b. The players are flawless in execution.
c. The players have sufficient intelligence to deduce the solution.
d. The players know the planned equilibrium strategy of all of the other players.
e. The players believe that a deviation in their own strategy will not cause deviations by any other players.
f. There is common knowledge that all players meet these conditions, including this one.
so, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on.
the conditions suppose that the players have answers to a variety of questions when entering the game.
what is your expected payoff? in what specific ways can it be maximized?
what is your 'solution?' what is the intended end result of the game?
how can your actions in the game and your understanding of the motivations of other players bring you closer to your maximized and expected payoff?
are there elements in play in your game that are being ignored, and therefore may disrupt this equilibrium?