Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 133

Problem with Beliefs

O2 Leave its current room and switch to room r 0 .
O3 Invite other agents to switch together to a certain room r i ,
which is achieved by the following four steps:
1. Select a room r i that is not already proposed before in the
current round by the proposing agent.
2. Select a set C of agents that are not currently in r i , and send a
proposal message to each, asking each recipient to indicate:
(1) whether he is interested in switching to r i .
(2) the minimum coalition size that must be achieved before he can
agree to switch to r i .
3. Upon receiving the response, try to construct a new coalition
structure CS 2 with the following four properties:
(1) The proposing agent is switched to r i (if it is not already in
r i at the beginning of the round) and that it prefers the resulting bid
b a|CS 2 to the current bid b a|CS .
(2) Amongst those agents that indicated they would consider a
switch, select zero or more of them to switch to r i together, such that
the resulting size of r i after the switches is no less than the requested
coalition size of each selected agent.
(3) The coalition structure CS 2 has not been proposed before by
any agent since the beginning of the mechanism.
(4) All other agents not selected remain in the same coalition as in
CS .
4. There are three possible subsequent actions:
(1) If such a new coalition cannot be constructed, then
• (Option 1) either choose to maintain status quo and the current
round continues, or
•

(Option 2) switch to r 0 and the current round ends.
(2) (Option 3) If such a new coalition can be constructed (the
proposal is said to be successful and this marks the end of a round),
send confirmation messages to the selected agents in (2) of the Step 3,
and broadcast the resulting new coalition structure CS 2 to all agents.