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>Gambit: Software Tools for Game Theory</TH
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><H1
><A
NAME="BIF.UNDOMINATED"
>UnDominated</A
></H1
><DIV
CLASS="REFNAMEDIV"
><A
NAME="AEN6757"
></A
><H2
>Name</H2
>UnDominated&nbsp;--&nbsp;Computes the undominated actions or strategies in a support</DIV
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><A
NAME="AEN6760"
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>Synopsis</H2
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CLASS="SYNOPSIS"
>UnDominated[support-&#62;NFSUPPORT, {strong-&#62;False}, 
            {mixed-&#62;False}, {precision-&#62;Rational}, {time&#60;-&#62;0.000000}, 
            {traceFile&#60;-&#62;(Output)}, {traceLevel-&#62;0}] =: NFSUPPORT 
UnDominated[support-&#62;EFSUPPORT, {strong-&#62;False}, {conditional-&#62;False}, 
            {time&#60;-&#62;0.000000}, {traceFile&#60;-&#62;(Output)}, 
            {traceLevel-&#62;0}] =: EFSUPPORT </PRE
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><A
NAME="AEN6762"
></A
><H2
>Description</H2
><P
><TT
CLASS="FUNCTION"
>UnDominated</TT
>
finds dominated strategies, or actions, as appropriate, in a 
<TT
CLASS="PARAMETER"
><I
>support</I
></TT
>.  The returned support contains only the undominated
strategies or actions; if this support is identical to the input support,
no strategies or actions were found to be dominated.  The following
optional parameters may be specified to modify the behavior of
the elimination:
<P
></P
><UL
><LI
><P
><TT
CLASS="PARAMETER"
><I
>strong</I
></TT
> By default, all weakly dominated strategies or actions
are eliminated.  If this is specified <TT
CLASS="LITERAL"
>True</TT
>, elimination is based
on strict dominance.</P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>mixed</I
></TT
>: By default, elimination is done in pure strategies or
actions.  If this is specified <TT
CLASS="LITERAL"
>True</TT
>, elimination is done by
examining mixtures over other strategies or actions.  Note that mixed 
elimination is only implemented for normal form games.  </P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>conditional</I
></TT
>: Dominance computations are conditional on
reaching infoset containing the action.  For example, a behavior
strategy may be strongly dominated conditional on reaching its
information set, but only weakly dominated in the entire game.  Only
relevant for extensive form games.</P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>precision</I
></TT
>: Default precision is rational.  Note that the precision
parameter is only applicable for mixed domination.  Pure strategy
domination always uses rational precision.</P
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