In fully cooperative games players will opt to form coalitions when the value of the payoff is equal to or greater than if they were to work alone.
Distributions where a player receives less than it could obtain on its own, without cooperating with anyone else, are unacceptable - a condition known as individual rationality.
For 2-player games the set of imputations coincides with the core, a popularly studied concept due to its stability against group deviations.
Nash bargaining theory, a type of cooperative bargaining, is used to solve this problem for 2-player games but will fail to yield any results for any games that are using more than two players,[2] this solution aims to maximise the pay off for both of the players.
[2] Schmeidler's Nucleolus refers to the imputation that minimizes the maximum excess, a min-max function.
Obviously, a rational player will leave the agreement if he/she can achieve a better outcome by abandoning, no matter what was announced before.
A number of regularization methods (integral and differential) based upon the IDP (imputation distribution procedures) was proposed.