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Problem with Beliefs
such that
b i b a i |CS .
If such a bid b exists, he should select Option 2.
3) Otherwise, he should select Option 1.
The b-strategy is similar to the nb-strategy, except that step 1 is
modified as follows:
If such a bid b exists and the agent has not already proposed
product g i in the current round, then he should select Option 3 and
send proposal messages to all agents a j such that bel i ( b j|CS j b j|CS ).
The two proposal strategies differ only in the list of agents that the
proposer should propose to. In the nb-strategy, the proposer proposes
to every agent that is not currently in the target room, whereas in the
b-strategy, the agent selectively proposes only to those agents which,
according to the proposer's private belief, will agree to switch to the
desired room. In the following, for ease of description, we shall label
agents employing the nb-strategy and b-strategy as nb-agents and b-
agents respectively.
For the recipient agents of the proposals, on the other hand, there
is only one rational strategy, that is, to accept the proposal if and only
if he prefers it to his current coalition, and to reject it otherwise. This
is described formally below.
An agent a j that receives a proposal to switch to room r i will
respond as follows:
1) First, the agent should check whether there exists a bid b =
( g i ,s ), where g i
is the product corresponding to room r i , such that
b
j b a j |CS .
2) If such a bid is found, the agent responds to the proposing agent
that he is interested, provided that the new coalition contains at least
s members. (If there are more than one such bids, choose one with the
smallest coalition size.)
3) If no such bid is found, then the agent indicates to the proposing
agent that he is not interested.
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