## Extreme games and their solutions |

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### Contents

Prelimi nari | 1 |

Convex Games | 11 |

Superaddi ti ve Games | 46 |

Copyright | |

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according affine set functions assume canonical representation classes coalition forming process consider core define equations extreme games extreme in F extreme point f 6 F f is extreme f o m f^o m f^om faom game theory given Hence holds true homl homogeneity implies indicator function inequalities Lemma linear ln other words ln view lndeed lt follows m,oc m(AK main simple solution marginal measure max max max mT max v(R maximal minimal representation mS(S n.d. hom natural numbers nondegeneracy nondegenerate Note Obviously player joining point functions problem production function production game production process Proof representation theory represented rescaling satisfied Seiten sequence Shapley value solution concept stable set Step superadditive games Suppose symmetric game Theorem 2.3 trivial uniform distribution unique units of money utility vector Vlll weighted majority xU'V zero sum