Multi-agent Cooperation and Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 5

then the social utilities are the total profits of all agents.
One of the natural solution concepts to multi-agent coalition for-
mation problem is to find solutions that can achieve, or approximate,
the maximal social utilities (called the social optimality). Therefore,
for multi-agent coalition formation mechanisms, the higher the social
utility of the produced solution is, the better the mechanism is, no
matter if some individual agents may actually suffer a loss.
But one problem here is that the social utility criterion assumes
that the individual agent's utilities can be meaningfully added up,
and one does not need to care about the individual agent's profit or
utility. But in reality, this is not always the case. So instead, the Pareto
Optimality concept is sometimes used in place of social utility.

1.1.2.2 Pareto Optimality

To overcome the shortcoming of social utility, some researches make
use of the Pareto optimality (or Pareto e ciency) criterion instead,
which was first proposed in 1906 by economist Vilfredo Pareto [10].
The idea here is that a solution is called Pareto optimal if it is not
possible for any agent to gain in utility without sacrificing at least one
of his fellow agents.
Thus, for coalition formation mechanisms, one possible goal is to
achieve as many Pareto optimal solutions as possible. In most cases,
Pareto optimality requires that there should be no left-over (unused)
utilities that can be assigned to the agent. So in some way, Pareto opti-
mal solutions are e cient, and the simplicity of the Pareto optimality
concept makes it a rather popular solution concept.

1.1.2.3 Drawbacks of Social Utility and Pareto Optimality

Social optimality and Pareto optimality are both nice features to have,
and in fact they have been used in evaluation of multi-agent coalition
formation (see Table 2.1). However, when used alone in the analysis of
multi-agent coalition formation mechanisms, neither one is sucient
for guaranteeing coalition stability.