<s>
In	O
other	O
words	O
,	O
is	O
a	O
submodular	B-Algorithm
set	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
A	O
submodular	B-Algorithm
utility	O
function	O
is	O
characteristic	O
of	O
substitute	O
goods	O
.	O
</s>
<s>
A	O
utility	O
function	O
is	O
additive	O
if	O
and	O
only	O
if	O
it	O
is	O
both	O
submodular	B-Algorithm
and	O
supermodular	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
is	O
a	O
subadditive	B-Algorithm
set	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Assuming	O
is	O
non-negative	O
,	O
every	O
submodular	B-Algorithm
function	I-Algorithm
is	O
subadditive	O
.	O
</s>
<s>
However	O
,	O
there	O
are	O
non-negative	O
subadditive	O
functions	O
that	O
are	O
not	O
submodular	B-Algorithm
.	O
</s>
<s>
In	O
other	O
words	O
,	O
is	O
a	O
superadditive	B-Algorithm
set	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
With	O
the	O
typical	O
assumption	O
that	O
,	O
every	O
submodular	B-Algorithm
function	I-Algorithm
is	O
subadditive	O
and	O
every	O
supermodular	O
function	O
is	O
superadditive	O
.	O
</s>
<s>
In	O
particular	O
,	O
if	O
a	O
submodular	B-Algorithm
function	I-Algorithm
is	O
not	O
subadditive	O
,	O
then	O
must	O
be	O
negative	O
.	O
</s>
<s>
A	O
unit-demand	O
function	O
is	O
an	O
extreme	O
case	O
of	O
a	O
submodular	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Every	O
GS	O
valuation	O
is	O
submodular	B-Algorithm
,	O
but	O
the	O
opposite	O
is	O
not	O
true	O
.	O
</s>
