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prefer playing tennis. The problem is that no one knows whether it is
going to rain in the afternoon, and their preferences (e.g., whether it
is better to play tennis or not to play tennis) depend on the uncer-
tain future state, that is, whether it will rain. Such uncertainty means
that the traditional core-based concept cannot be readily used to anal-
yse the game. Normally, such uncertainty does not defer coalitions to
be formed in the real world. For example, Ivy and Jill might agree
that they will decide to wait until 1 o'clock before they make the final
decision on whether or not to play tennis.
To deal with this problem, let us consider how such uncertainty is
dealt with by human beings in the real world. Instead of evaluating a
proposed coalition by predefined preferences or publicly known values,
as done in traditional game theoretic approaches, real world agents
tend to rely on various available information from their previous expe-
rience to predict the future state , based on whatever information they
can currently observe or have observed. Their decision will then be
based on the (generally uncertain) predictions.
Example 3.2 In the retail market, a seller (e.g., a department store)
often offers to give a large discount for bulk purchases. That is, if the
seller can sell a large number of the same item at one time, then he
can probably be willing to sell the items at a discounted price. Nor-
mally, when the number of items is larger, the discount rate is higher.
Therefore, customers have the incentive to form buyer coalitions so as
to buy a large number of the same items from a seller at a time [1, 2]
and enjoy a large volume discount.
Supposed that there are multiple on-line sellers offering a certain
type of products, and a number of on-line buyers agents are negotiating
to form coalitions to buy items from the on-line sellers (for example,
they may form groups in order to obtain volume discounts). As in most
multi-agent applications, the agents are not omniscient. Therefore, the
agents need to continuously observe the environment they are situated
in, update their private beliefs accordingly, and act according to their
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