Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 140

other approach only achieves core-stable result in 93% of the test cases
on average. The DNCF mechanism has passed the stability criterion.
Our result is also good for the Pareto optimality criterion as we also
obtain Pareto optimal results in over 99% of the cases.

105
100
95
90

DNCF all b-agents
DNCF all nb-agents
DNCF mixed agents
[3]

85
80
75

4 6 8 10

Number of Agents

Fig. 5.3 Percentage of results in b-core.

We then investigate on the scalability of DNCF by extending the
experiment to include up to 30 agents. The setting of this experiment
is the same as above, except that each test case is now repeated twice
with all agents being b-agents and all agents being nb-agents respec-
tively. The total number of messages sent is recorded.
The result is shown in Figure 5.4, which suggests that the rate
of growth of number of messages with respective to the number of
agents is close to linear for both the b-agents and the nb-agents cases,

Fig. 5.4 Number of messages sent.