Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 35

always more preferable than two tennis coalitions of two tennis players
each. We also assume that all agents in the same coalition perform the
same activity (playing tennis or watching movie). That is, we do not
allow some agents in a group to watch movie while some others play
tennis, or vice versa, otherwise they cannot be said to be in a group.
Finally, for ease of analysis, we assume that if any agents decide to play
tennis, they do not need to go in groups of even number of players,
with an understand that this is always possible if we assume that an
agent can always go to play tennis in a tennis club where a partner is
not di culty to find.

Tab l e 3 . 1 Preferences of Agents

A 1 A 2 A 3 A 4

Good Movie Movie Movie Movie

Average Movie Movie Tennis Tennis

Bad Tennis Tennis Tennis Tennis

Such scenario is very common in daily life. The main problem here
is that those preferences are actually uncertain, in the sense that they
depend on the quality of the movie, which is unfortunately unknown
at the time of consideration. To overcome this problem, suppose that
the agents keep records of the movies they have seen before, as shown
in Tables 3.2 to 3.5. Each table records the director, movie type and
quality of the movies in an agent's viewing history. Agent A 1 , A 2 , A 3 ,
and A 4 uses the data in different tables to predict the quality of current
movie. For example, agent A 1 will have the opinion that the current
movie, being an S.F. movie directed by Spielberg, is likely to be good
since the quality of all similar cases in his experience (see Table 3.2)
are good. Agent A 2 probably will have the same expectation, while
the opinions of agents A 3 and A 4 might be different.
The concept of representing information in decision tables, as done
in Tables 3.2 to 3.5, has been studied by many authors [5, 6]. Formally,