Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 43

• The state H is the quality of the movie, the possible values of

which are members of the set V H (but

the prevailing state s ∗ for the current game is to be determined).

= { Good , Average , Bad }

• ( I i ) is as shown in Tables 3.2 to 3.5. For example, agent A 1 's ex-

perience I 1 as shown in Table 3.2 has 9 rules, which are

(Director = Spielberg) ∧ (Type = S.F.) ⇒ Good

(Director = Spielberg) ∧ (Type = Biographic) ⇒ Good

(Director = Spielberg) ∧ (Type = S.F.) ⇒ Good

(Director = Coppola) ∧ (Type = Drama) ⇒ Good

(Director = Tempa) ∧ (Type = Action) ⇒ Bad

(Director = Emmerich) ∧ (Type = S.F.) ⇒ Bad

(Director = Sonnenfield) ∧ (Type = S.F.) ⇒ Good

(Director = Spielberg) ∧ (Type = S.F.) ⇒ Good

(Director = Spielberg) ∧ (Type = Drama) ⇒ Average

• Some of the possible consequences for this coalition are (tennis, ten-

nis, tennis, tennis), (tennis, tennis, movie, movie), (movie, movie,
movie, movie) . . . .

• P i is agent i 's set of preference rules. Intuitively, each rule de-

termines part of the agent i 's preference, given the states in the
agent's experience I i that supported by the current evidences E .
For example, as currently

E = { (Director = Spielberg) ∧ (Type = S.F.) },

by agent A 1 's experience I 1 the supported states are members of
the set

{ Good , Good , Good } = { Good } .

As we assume that 'if the movie is good, then all four agents prefer
the movie over tennis,' we would expect that P 1 contains, among