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ferent strategies in the mechanism illustrated in Figure 4.4. Type-n
agents, when selected to make proposals, do
not
consider his beliefs
about the other member's preference (i.e., he does not care whether
his proposal is likely to be accepted or not, and just proposes it as
long as he thinks it is beneficial to himself), while the second type
of agents (type-b) carefully propose only the ones that are consistent
with their beliefs (i.e., the agent only proposes those proposals which
he thinks will be accepted). The actions of these two types of agents
are summarised as shown in Figure 4.7.
Strategy of type-n (non-belief-based) agents
In step 2 of the mechanism in Figure 4.4, the agent finds and proposes an alter-
native coalition such that:
•
The proposing agent is a member of a coalition
C
.
•
The proposing agent prefers the coalition
C
to
C
.
Strategy of type-b (belief-based) agents
In step 2 of the mechanism in Figure 4.4, the agent finds and proposes an alter-
native coalition such that:
•
The proposing agent is a member of a coalition
C
.
The proposing agent prefers the coalition
C
to
C
.
•
The proposing agent
believes
that all member of
C
would prefer the coalition
C
to
C
.
•
Fig. 4.7
Type-n agents and Type-b agents.
We perform an experiment involving six agents, whose preferences
regarding the candidate coalitions are randomly ordered. Each agent
also has a belief of each other's preference, but subjected to a 25%
error rate: for any two agents
i
and
j
, and for any two coalitions that
involve both agents, there is a 25% chance that agent
i
is wrong about
agent
j
's preference order regarding those two coalitions. Each game is
repeated twice: first with all agents being type-n (labelled as Random-
N games), then with all agents being type-b (labelled as
Random-B
games, and the number of stable outcomes are counted.
The results are shown in Figures 4.8 and 4.9. In Figure 4.8, we
see the percentage of games that reach a stable coalition structure
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