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strong cores would be all empty of the weak core of any of the games
is empty.
weak-cores
core
strong-cores
Fig. 3.4 Illustration of Theorem 3.4.
3.7 Application Areas
In this last section, we summarize several application areas where we
believe the proposed criteria can provide a useful solution concept.
Applications in non-transferable utility game
While existing probabilistic approaches define stability concepts on an
important class of uncertain coalition games with transferable utility,
there are many applications where it is more natural to describe the
game in terms of agents' preference instead of transferable utilities.
For example, in the Example in Section 3.2, it would be su cient
for an agent to simply state 'I prefer movie to tennis if the movie is
good' instead of stating 'My utility for the movie is 0.5, whereas my
utility for tennis is 0.2, given that the quality is good'. And even if the
utilities are stated in the latter way, there are likely not transferable
utilities. The problem here is, of course, the probabilistic approaches
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