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for changes to the coalition structure such that (1) a new coalition
is formed in the alternative outcome, where the proposing agent is
a member, (2) the proposing agent is better off in the new coalition
than previously. The new outcome becomes effective if the proposal
is accepted by every members of the new coalition. The mechanism
terminates after a pre-defined number of rounds is reached (termina-
tion by time) or if no new proposals are accepted for a pre-defined
consecutive number of rounds (termination by stagnant criterion). For
simplicity, we assume there is only one possible action per coalition in
this example.
We now look at an example dating game involving three agents,
a
,
b
,and
c
, who are considering to watch a movie together.
Example 4.3 (A belief-based dating game)
Three agents,
a
,
b
,
and
c
, are considering to watch a movie together. Their preferences are
that each of them prefers to go in pairs (coalition of size 2) if possible.
Failing that, their next choice is to go in a group of all three, and their
least preferred choice is to go alone. Furthermore, among the coali-
tions of size 2, agent
a
prefers to go with agent
b
, but agent
b
prefers
to go with agent
c
, and finally, agent
c
prefers to go with agent
a
.In
summary, their preferences are shown in Figure 4.2.
Agent
a
's preference:
(
{a, b},
movie)
a
(
{a, c},
movie)
a
(
{a, b, c},
movie)
a
(
{a},
movie)
Agent
b
's preference:
(
{b, c},
movie)
b
(
{a, b},
movie)
b
(
{a, b, c},
movie)
b
(
{b},
movie)
Agent
c
's preference:
(
{a, c},
movie)
c
(
{b, c},
movie)
c
(
{a, b, c},
movie)
c
(
{c},
movie)
Fig. 4.2
Three agents' preferences.
The game is depicted in Figure 4.3, where each node represents
a possible coalition structure. For example, the top left node
{
(
{
a
}
,
movie), (
represents the coalition struc-
ture where each agent forms his own singleton coalition and goes to
{
b
}
,movie),(
{
c
}
,movie)
}
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