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Respond to the question: How is the core stable?

11/30/2006 03:54 AM by Azadeh; How is the core stable?
I'll be very thankful if you concern this:

The core -by definition of Osborn's book- is the set of payoff vectors for all playes which no other group of players improve upon. i.e. no other geoup can provide more payoffs for all of its members than the grand coalition.

My question is:
Assume that we have a game of 4 players playing cooperatively.
Consider we have a feasible payoff vector xi=(1,2,3,8) and we claim that it is in the core.
Finding a group of 3 players(for example) which divides the worth between its players like this: (2,7,3) or (2,8,2) for the first three players does not deny the membership of xi in the core which offers them (1,2,3) (by definition).
It means despide the possibility of forming the latter three member group, the grand coalition will form and it will be stable.
Is that logical or am I wrong?

That is players 1 and 2 really prefer membership in the latter coalition than the grand coalition and it is this coalition which will form practically. So were is the stability of the Core?

thanx a lot
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