Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 132

5.3.1 Distributed Non-transferable Utility Coalition

Formation Mechanism

Consider an NTU-Buyer game

g = N,G, ( i ) ,B

with a set

N = { 1 , 2 ,...,n }

of players and a set

G = {g 1 ,g 2 ,... g m }

of goods. For ease of description, we suppose there are m +1 rooms
labelled r 0 ,r 1 ,...,r m respectively. The rooms r 1 ,...,r m function as
virtual gathering places for agents currently interested to join the coali-
tion to buy the i -th product, whereas the remaining room r 0 functions
as a non-cooperative room, meaning the agents in this room will buy
the items individually instead of buying in a group. Initially, all agents
are in r 0 .
For simplicity, in the following discussion, we will use the phrase
'agent a is in room r i ' as a synonym for 'agent a is in the buyer
coalition for product g i ,' and 'agent a switches to room r i 'tomean
that 'agent a , which is currently not in the coalition for g i ,leavesits
current coalition and joins the coalition for product g i ,' and 'size of
room r i ' as a synonym for 'size of coalition for the product g i ,' except
for the room r 0 , which does not represent any coalition.
The agents are randomly asked to make proposals in turn. The
mechanism is divided into rounds, and the current coalition structure
at the beginning of a round is labelled CS . In turns, each agent a
performs either one of the following three options, according to the
proposal order:
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O1 Do nothing and maintain the status quo.