1,084 research outputs found
The Maximal Payoff and Coalition Formation in Coalitional Games
This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then provides answers to the questions of what payoffs to split, how to split the payoff, what coalitions to form, and how long each of the coalitions will be formed by rational players in coalitional TU games. Finally, it obtains analogous results in coalitional NTU (non-transferable utility) games.Coalition Formation, Core, Maximal Payoff, Minimum No-Blocking Payoff
Solutions of some Monge-Amp\`ere equations with isolated and line singularities
In this paper, we study existence, regularity, classification, and
asymptotical behaviors of solutions of some Monge-Amp\`ere equations with
isolated and line singularities. We classify all solutions of in with one puncture point. This can be applied to characterize
ellipsoids, in the same spirit of Serrin's overdetermined problem for the
Laplace operator. In the case of having non-removable singular points for
, modulo affine equivalence the set of all generalized solutions can be
identified as an explicit orbifold of finite dimension. We also establish
existence of global solutions with general singular sets, regularity
properties, and optimal estimates of the second order derivatives of
generalized solutions near the singularity consisting of a point or a straight
line. The geometric motivation comes from singular semi-flat Calabi-Yau
metrics.Comment: 25 page
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