<s>
The	O
round-robin	B-Algorithm
protocol	I-Algorithm
requires	O
additivity	O
,	O
since	O
it	O
requires	O
each	O
agent	O
to	O
pick	O
his	O
"	O
best	O
item	O
"	O
without	O
knowing	O
what	O
other	O
items	O
he	O
is	O
going	O
to	O
get	O
;	O
additivity	O
of	O
valuations	O
guarantees	O
that	O
there	O
is	O
always	O
a	O
"	O
best	O
item	O
"	O
(	O
an	O
item	O
with	O
a	O
highest	O
value	O
)	O
.	O
</s>
<s>
The	O
round-robin	B-Algorithm
protocol	I-Algorithm
is	O
very	O
simple	O
to	O
execute	O
:	O
it	O
requires	O
only	O
m	O
steps	O
.	O
</s>
<s>
An	O
alternative	O
algorithm	O
,	O
which	O
may	O
attain	O
a	O
higher	O
social	O
welfare	O
,	O
is	O
the	O
Iterated	O
maximum-weight	B-Algorithm
matching	I-Algorithm
algorithm	O
.	O
</s>
<s>
In	O
each	O
iteration	O
,	O
it	O
finds	O
a	O
maximum-weight	B-Algorithm
matching	I-Algorithm
in	O
the	O
bipartite	O
graph	O
in	O
which	O
the	O
nodes	O
are	O
the	O
agents	O
and	O
the	O
items	O
,	O
and	O
the	O
edge	O
weights	O
are	O
the	O
agents	O
 '	O
values	O
to	O
the	O
items	O
.	O
</s>
<s>
Note	O
that	O
even	O
iterated	O
maximum-weight	B-Algorithm
matching	I-Algorithm
does	O
not	O
guarantee	O
Pareto	O
efficiency	O
,	O
as	O
the	O
above	O
allocation	O
is	O
dominated	O
by	O
(	O
xwv	O
,	O
zyu	O
)	O
with	O
utilities	O
(	O
19	O
,	O
36	O
)	O
.	O
</s>
<s>
The	O
round-robin	B-Algorithm
protocol	I-Algorithm
guarantees	O
EF1	O
when	O
the	O
items	O
are	O
goods	O
(	O
-	O
valued	O
positively	O
by	O
all	O
agents	O
)	O
and	O
when	O
they	O
are	O
chores	O
(	O
-	O
valued	O
negatively	O
by	O
all	O
agents	O
)	O
.	O
</s>
<s>
However	O
,	O
combining	O
round-robin	O
with	O
the	O
envy-graph	B-Algorithm
procedure	I-Algorithm
gives	O
an	O
algorithm	O
that	O
finds	O
allocations	O
that	O
are	O
both	O
EF1	O
and	O
satisfy	O
the	O
cardinality	O
constraints	O
.	O
</s>
