The Complete Picture: sb-core and wb-core - Belief-based Stability in Coalition Formation with Uncertainty - page 148

not modelled in the traditional games stability concepts such as the
core. In this chapter, we develop these concepts one step further by
investigating games with both type of uncertainties.
6.2 An Illustrating Example
In this section we illustrate the ideas more clearly by studying an
example where agents' decision is affected by both private beliefs and
uncertain opinions.
Example 6.1 Three agents a , b ,and c , representing the interest of
three mobile phone companies, are considering to enter the 4G LTE
phone market in a country. However, given the current global financial
situation, they are not certain whether the new technology will be well
received by the consumers. For practical consideration, both companies
assume that there can only be two different type of outcomes: that the
phones are well received (with sales level surpassing a certain threshold
amount) or not, which are represented by environmental states s 1 (the
phones are well received) and s 2 respectively (the phones are not well
received).
However, the two agents have different preferences depending on
the environmental state which they believe the world is in. The pref-
erences of the two agents, which are described in Figure 6.1, are repre-
sented by total ordered relations on the set of coalitions, of which the
agents are members.
Fig. 6.1 Agent preferences in Example 6.1.