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Example 6.6
Let
g
1
be the game in Example 6.1. Let
g
3
be another
game that is identical to
g
1
,exceptthattheagent
a
's external belief is
now more accurate: he now correctly believe that all three agents po-
tentially prefer the coalition
{a, b, c}
to the singleton coalitions where
each of them is on their own. Then for
g
3
,wehave
wb-core(
g
3
)=
{{{
a
}
,
{
b
}
,
{
c
}}
,
{{
a, b, c
}}}
as before, but sb-core(
g
3
)isnowempty.
6.5 Summary
Most classical solution concepts in non-transferable utility coalitional
game theory rely on a common information assumption. That is, they
assume the agents' preferences to be publicly known, and that each
agent is certain about their preferences. However, this assumption is
not practical in many software agent applications where intelligent
agents have to rely on their private beliefs during decision making.
In this chapter, we extend the concepts proposed in Chapters 3 and
4, and propose a new type of games which we label belief-based non-
transferable utility games with beliefs and uncertainty, and provide
new solution concepts for describing the stability of coalitions these
games, namely, the sb-core, wb-core, s-core and w-core.
References
[1]
Bratman M E. Intention, Plans, and Practical Reason. University of Chicago
Press, 1999.
[2]
Seow K T. Coalition formation for resource coallocation using bdi assign-
ment agents. IEEE Transactions on Systems, Man, and Cybernetics, Part C:
Applications and Reviews, 37(4): 682-696, 2007.
[3]
Seow K T. Collaborative assignment using belief-desire-intention agent mod-
eling and negotiation with speedup strategies. Information Sciences: an In-
ternational Journal, 178(4): 1110-1132, 2008.
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