Multi-agent Cooperation and Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 4

ment of the global output, such as the total profit, as an indication of
solution quality, if the problem is a purely cooperative one (because
in a purely cooperative problem, there is no issue with the benefits
of individual agents, and no agent will break away from the alliance
because of insu cient payment).
However, in semi-competitive games, the guarantee of a good global
solution is not su cient. In these problems, the real concern is often
the stability of the coalitions (e.g., does any agent have the incentive
to break away from the alliance because he thinks that the payment
is not good enough?).
These arguments lead to the following solution concepts from eco-
nomics, namely social optimality and Pareto optimality. Both concepts
are frequently employed in studies of coalition formation problems, and
are described in the next subsection.

1.1.2 Two Basic Solution Concepts of Coalition Formations

Several well known solution concepts in economics exist, and are in-
deed used in studies of coalition formation mechanisms by multi-agent
researchers.
One of such basic criteria is the social utility criterion. According
to the utility theory in economics (see, for example, [9]), the personal
preferences of each agent regarding the possible outcomes can be rep-
resented by real numbers known as the utilities of the agents, so that
the larger is the utility, the higher is the preference for some particular
solution.

1.1.2.1 Social Utility

Under several assumptions, such as the completeness, transitivity, con-
tinuity of the preferences, and transferability of the utility, the utilities
of various agents can be added up into the social utility of the system.
Thus, if the utilities are defined as the profit of the individual agents,