The b-Core: Belief-based Coalition Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 88

( { Mary } , Domani ) } ,

( { Mary } , Yung Kee ) } ,

( { John , Mary } , Bonheur Restaurant ) } ,

( { John , Mary } , Sashimi Hiro ) } ,

( { John , Mary } , Jashan ) } ,

( { John , Mary } , Spasso ) } ,

( { John , Mary }, Domani ) },

( { John , Mary }, Yung Kee ) }.

Both preference John and Mary are so defined that ( { John , Mary },
Yung Kee ) is more preferred to any other coalitional acts.

• Both private beliefs bel John and bel Mary in B are defined as follows.

If α 1 John α 2 ,then bel Mary ( α 1 John α 2 ), except that we replace
all occurrences of

bel Mary (( { John , Mary } , Yung Kee ) John α )

by

bel Mary (( { John , Mary } , Bonheur Restaurant ) John α )

for any α . Similarly, if α 1 Mary α 2 ,then bel John ( α 1 Mary α 2 ),
except that we replace all occurrences of

bel John (( { John , Mary } , Yung Kee ) Mary α )

by

bel John (( { John , Mary } , Bonheur Restaurant ) Mary α )

for any α . 1

1 Arguably we should also replace all occurrences of bel Mary (( { John } , Yung Kee )
John α )by bel Mary (( { John }, Bonheur Restaurant ) John α ) for any α (and simi-
larly for bel John ), but this does not affect the results of analysis.