proved by altering his decision unilaterally.
The roles of all players are symmetric in the
sense that they make their decisions indepen-
dently and none of them dominates any other.
If
J
i
, i = 1, 2, . . . , N is a cost function of
ith player in N-person game and d
i
his strat-
egy then N-tuple
d
∗
1
, d
∗
2
, . . . , d
∗
N
constitutes
a Nash equilibrium solution if
J
1
d
∗
1
, d
∗
2
, . . . , d
∗
N
≤ J
1
d
1
, d
∗
2
, . . . , d
∗
N
J
2
d
∗
1
, d
∗
2
, . . . , d
∗
N
≤ J
2
d
∗
1
, d
2
, . . . , d
∗
N
...
J
N
d
∗
1
, d
∗
2
, . . . , d
∗
N
≤ J
N
d
∗
1
, d
∗
2
, . . . , d
N
for any admissible
d
i
; i = 1, 2, . . . , N. The
nonzero-sum game may admit more than one
Nash equilibrium solution with outcomes
different in each case. Since the total order-
ing among N-tuples of numbers does not ex-
ist, it is usually not possible to declare one
of them as the most favorable. Nevertheless,
some of strategies may be viewed as better
than other ones if the respective outcomes
are in partial order. With this notion of bet-
terness, a Nash equilibrium strategy N-tuple
is admissible if there exists no better one. In
the case when the game is played, many times
in the same conditions, the Nash equilibrium
may be defined for average values of the cost
functional and mixed strategies.
NASTRAN
a widely used computer code
for mechanical and structural analysis, such
as for opto-mechanical and thermal analyses.
National Electrical Code (NEC)
a stan-
dard for electrical construction, published
by the National Fire Protection Association
(NFPA 70-1). The National Electrical Code
is often adopted by local jurisdictions and
used by their electrical inspectors.
National Electrical Manufacturers Asso-
ciation (NEMA)
an electrical trade as-
sociation that establishes standards for elec-
trical equipment. In the case of electric mo-
tors, NEMA establishes standard frame sizes,
starting torque, starting current, and other
quantities for a given horsepower machine.
National
Fire
Protection
Association
(NFPA)
sponsor and publisher of the Na-
tional Electrical Code and other safety stan-
dards.
National Television System Committee
(NTSC)
a body that recommended the
standard for colored television broadcasts in
the U.S. in 1953. NTSC video contains 525
lines, a field rate of 59.94 fields/second, a
horizontal frequency of 15,734.264 Hz, and
an interlaced color subcarrier frequency of
3.579545 MHz. The NTSC format is also in
use by many countries other than the U.S.
natural broadening
spectral broaden-
ing of a transition in a laser medium due
to spontaneous decay; sometimes called life-
time broadening.
natural commutation
commutation of
current from one switching device to another
in a power electronics converter at the instant
the incoming voltage has a higher potential
than that of the outgoing wave, without the
aid of any commutation circuitry. See also
commutation
.
natural constraint
constraint that results
from the particular mechanical and geomet-
ric characteristics of the task configuration.
Used to define a particular situation occurring
between the manipulator end-effector and the
work environment. These constraints are de-
fined in terms of linear and angular veloci-
ties and forces and/or torques that are speci-
fied to execute the task. Natural constraints
are intrinsically associated with the particu-
lar task. For example, consider a task that
an end-effector moves along a rigid surface
and is not free to move through that surface.
In this particular situation, a natural position
constraint exists. In addition, if the surface
is frictionless, the end-effector is not free to
apply arbitrary force tangent to the surface,
and hence a natural force constraint exists.
natural frequency
the frequency of any
oscillating term in the response of the linear
c
2000 by CRC Press LLC