Abstract
We study the nucleolus of veto games (see Bahel in Int J Game Theory 45(3):543–566, 2016), where some players are indispensable for coalitions to achieve a positive value. We first derive some noticeable properties satisfied by the nucleolus of a veto game: for instance, veto players always receive a higher payoff than the others. In the particular case of clan games, Potters et al. (Games Econ Behav 1:275–293, 1989) provided a formula for the nucleolus. We give a condition that is necessary and sufficient for this formula to apply in a general veto game. Building on this result, we describe an intuitive adjustment process allowing to derive a generic formula for the nucleolus of a veto game.
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