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A class of coalitional games of particular interest are those known as S-veto games. In these, a coalition is only effective if some subset S of the players are all members. Thus this gives rise to characteristic functions of the form

wS(T) =    1    S ⊆ T
                  0   otherwise

For instance, S = {1} gives rise to a dictatorship by Player 1 (an inessential game) whereas S = X forces the grand coalition to form for any player to receive a payoff- or, considered as a voting system, a unanimous verdict. More complicated voting arrangements can be built upon veto systems, such as the United Nations Security Council system of 'great power unanimity' which requires the support of all five permanent members (and any four of the ten non-permanent members) to pass major resolutions.

Mathematically, the S-veto games serve as a basis for the space of all coalitional form games; this enables a proof of uniqueness for the Shapley function.


Part of A survey of game theory- see project homenode for details and links to the print version.

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