A strategy is, therefore, dominant, if: (1) each player is
getting more under the strategy than under any other strategy and (2)
the players in the coalition receive a total payment that does not
exceed the value of the coalition. Rational players are likely to
prefer the dominant strategy and to enforce it. Thus, the solution to
an n-players game is a set of imputations. No single imputation in the
solution must be dominant (=better). They should all lead to equally
desirable results. On the other hand, all the imputations outside the
solution should be dominated. Some games are without solution (Lucas,
1967).
Auman and Maschler tried to establish what is the right payoff to the
members of a coalition. They went about it by enlarging upon the
concept of bargaining (threats, bluffs, offers and counter-offers).
Every imputation was examined, separately, whether it belongs in the
solution (=yields the highest ranked outcome) or not, regardless of the
other imputations in the solution. But in their theory, every member
had the right to "object" to the inclusion of other members in the
coalition by suggesting a different, exclusionary, coalition in which
the members stand to gain a larger payoff.
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