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preferences, while the dotted lines represent the 'wrong' objections due
to the players' incorrect belief. It can be seen that the coalition struc-
ture
should be the only stable one accord-
ing to the players' actual belief, while only
{
(
{
John
,
Mary
}, Bonheur
Restaurant
)
}
is stable with the 'wrong' objections.
{
(
{
John
,
Mary
}
, Yung Kee
)
}
({John, Mary},
Sashimi Hiro
)
({John, Mary},
Bonheur
Restaurant
)
({John, Mary},
Jashan
)
({John, Mary},
Spasso
)
({John, Mary},
Yung Kee
)
({John, Mary},
Domani
)
Fig. 4.6
The belief-based game of John and Mary.
In the following, we illustrate how the concept of belief-based sta-
bility can be applied in analysis of coalition formation mechanism.
In most distributed coalition formation mechanisms that employ
propose-and-evaluate type protocols, one decision problem faced by
the agents is what to propose to other agents. This can be problem-
atic in situations where agents process only private beliefs instead of
common knowledge, because the agent has no way of knowing whether
his proposal is acceptable to other agents or not. Naturally, one strat-
egy for the agents is to only make proposals that are
consistent with
their belief
regarding other agent's preferences. The goal in the follow-
ing example is to study the impact of such a strategy on the coalition's
stability and speed of convergent to a stable solution.
Example 4.6 (A randomised coalition formation mechanism)
In order to investigate the effect of agent beliefs, we assume that there
are two types of agents, namely type-b and type-n agents, with dif-
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