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Implementation theory is an area of game theory closely related to mechanism design where an attempt is made to add into a game a mechanism such that the equilibrium of the game conforms to some concept of social optimality (for instance Pareto optimality).
In a game where multiple agents are to report their preferences (or their type), it may be in the best interest of some agents to lie about their preferences. This may improve their payoff, but it may not be seen as a fair outcome to other agents. In order to implement a more "fair" outcome, in a repeated game, the other players may choose to punish any "cheaters".
The conditions of a repeated game where an arbitrary outcome may be enforced are set out in theorems often known as folk theorems. If a game is not repeated, it may only be possible to implement outcomes which are Nash equilibria or satisfy some other equilibrium concept.