The b-Core: Belief-based Coalition Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 75

more proposals, or a pre-defined time limit is reached. But in any
cases, there are frequently time constraints and other limitations (e.g.,
problem size) during the propose-and-evaluate process, which means,
in practice, that the agents can only make those proposals that have
a reasonable chance of being accepted, according to the beliefs of the
proposing agent. Indeed, raising a proposal that have no chance of
being accepted according to one's beliefs should be considered as irra-
tional, and such behaviour should not occur in the world of software
agents. Thus, during such a process, if a point is reached, such that
each agent believes there is no better alternative solution than the cur-
rent arrangement, for both himself and his (potential) partners, then
the current solution should be regarded as stable, no matter whether
those beliefs are accurate or not.

Example 4.2 The unfortunate event that you and Mary end up
having dinner at Bonheur Restaurant might be the result of the fol-
lowing propose-and-evaluate type of coalition formation mechanism:
•

You: Hi Mary! How are you doing? Sorry for calling you so early
in the morning.

• Mary: I'm fine. You really get up very early in the morning.

• You: I wonder whether you would have some time this evening.

• Mary: Yes?

• You: I know that there is a very good Japanese restaurant Sashimi

Hiro that specialises in sashimi ... .

• Mary: Sashimi? I do not think I am not that keen on raw fish.

You know, they are raw.

• You: Really? Well, what do you think about Indian food?

• Mary: This is good, except that the Indian restaurants are all very

far away except Jashan .ButIwasin Jashan once and it was not
very good. The murgh makhani was terrible.

• You: Then shall we try Spasso ... .

• Mary: I just went to Domani yesterday with some old friends.

• You: O.K., O.K. What about Bonheur Restaurant ?Iknowthey