The b-Core: Belief-based Coalition Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 97

reason is that for , there are no other coalitional act

profiles that both i) dominate it and ii) dominate it based on belief.
However, it should be noted that

{ ( { a, b, c } , movie) }

is actually dom-
inated by all the coalitional act profiles with coalitions of size 2, only
that there is no coalitional act profile that dominates it based on belief.
Intuitively, this means that the three agents a , b ,and c will be happy
to go together to see the movie, although in their hearts they really
wish to go to see the movie in pairs. The only reason why they do not
propose to go in pairs is that they do not believe that such proposals
will be effective objections.

{ ( { a, b, c } , movie) }

Example 4.19 Consider again Example 4.6. This time, we mea-
sure the percentage of stable outcomes according to the concept of b-
core, out of 1000 repetitions, achieved after various numbers of rounds.
The result, as shown in Figure 4.10, suggests that belief-based games
(Random-B) achieves larger number of stable results than the non-
belief-based games (Random-N) throughout the execution of the mech-
anism, which is consistent with our previous observation in Figure 4.9.
In fact, by comparing Figure 4.8 and Figure 4.10, we now know that
Random-B games converge to a result in the b-core, whereas Random-
N games converge to the traditional core. This experiment, although

100
90
80
70
60
50
40
30
20
10
0

20 50 100 150 200 250 300 350 400 450 500

Number of rounds
Random-N Random-B

Fig. 4.10 Comparison of games populated with type-b and type-n agents,
using the b-core criterion.