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Coreness of Cooperative Games with Truncated Submodular Profit Functions
Coreness represents solution concepts related to core in cooperative games,
which captures the stability of players. Motivated by the scale effect in
social networks, economics and other scenario, we study the coreness of
cooperative game with truncated submodular profit functions. Specifically, the
profit function is defined by a truncation of a submodular function
: if and
otherwise, where is a given threshold. In this paper, we
study the core and three core-related concepts of truncated submodular profit
cooperative game. We first prove that whether core is empty can be decided in
polynomial time and an allocation in core also can be found in polynomial time
when core is not empty. When core is empty, we show hardness results and
approximation algorithms for computing other core-related concepts including
relative least-core value, absolute least-core value and least average
dissatisfaction value
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