Thus, we have proved that the solution of system
(5) describes the equilibrium. The equilibrium is
stable. Indeed, if, for instance, the actor A chooses the
emission , which differs from the equilibrium value
,
then the value of his utility function
will be
higher than the value of this function in the equilibrium.
The stability is a very important argument in the process
of selection among different virtual decision makings.
This principle (stability) guarantees the ``fair play''
since none of the actors has an advantage to depart from the
accepted agreement (equilibrium).
Nevertheless, one problem appears: is the suggested
choice efficient? In other words, would there be another choice,
which is more advantageous for both actors than the
equilibrium one? It is proved that the equilibrium
solution is efficient, i.e., it can not be improved for
both actors simultaneously, and the solution belongs to
the Pareto's set. If we would prove that decreasing, for
instance, , we necessarily increase
, then by the same
token the main statement is proved.
Let and
satisfy the conditions (4), hence, they
are the solution of (5). Let us try to decrease the
value
changing only
. Since in
the equilibrium
then by increasing
we
get
, and
increases. On the contrary, if we
decrease
then
, and
increases also.
We can decrease
only if we decrease
, but this
implies an increase of
. Therefore, the equilibrium
solution is efficient and the point
belongs to
the Pareto's set.
Note that all these results come from a partial
application of the general theory mentioned in [4].
Speaking about an application of the game theory to the
problem of CO emissions and their reductions we must say
a few words about other approaches.