File: bif.liapsolve.html

package info (click to toggle)
gambit-doc 0.97.0-1
links: PTS
area: main
in suites: etch, etch-m68k, lenny, sarge, squeeze
size: 1,344 kB
sloc: makefile: 19; sh: 10
file content (255 lines) | stat: -rw-r--r-- 4,411 bytes
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
<HTML
><HEAD
><TITLE
>LiapSolve</TITLE
><META
NAME="GENERATOR"
CONTENT="Modular DocBook HTML Stylesheet Version 1.59"><LINK
REL="HOME"
TITLE="Gambit"
HREF="gambit.html"><LINK
REL="UP"
TITLE="Built-in functions"
HREF="c2106.html#GCL.BUILTIN"><LINK
REL="PREVIOUS"
TITLE="LessEqual"
HREF="bif.lessequal.html"><LINK
REL="NEXT"
TITLE="LiapValue"
HREF="bif.liapvalue.html"></HEAD
><BODY
CLASS="REFENTRY"
BGCOLOR="#FFFFFF"
TEXT="#000000"
LINK="#0000FF"
VLINK="#840084"
ALINK="#0000FF"
><DIV
CLASS="NAVHEADER"
><TABLE
WIDTH="100%"
BORDER="0"
CELLPADDING="0"
CELLSPACING="0"
><TR
><TH
COLSPAN="3"
ALIGN="center"
>Gambit: Software Tools for Game Theory</TH
></TR
><TR
><TD
WIDTH="10%"
ALIGN="left"
VALIGN="bottom"
><A
HREF="bif.lessequal.html"
>&#60;&#60;&#60; Previous</A
></TD
><TD
WIDTH="80%"
ALIGN="center"
VALIGN="bottom"
></TD
><TD
WIDTH="10%"
ALIGN="right"
VALIGN="bottom"
><A
HREF="bif.liapvalue.html"
>Next &#62;&#62;&#62;</A
></TD
></TR
></TABLE
><HR
ALIGN="LEFT"
WIDTH="100%"></DIV
><H1
><A
NAME="BIF.LIAPSOLVE"
>LiapSolve</A
></H1
><DIV
CLASS="REFNAMEDIV"
><A
NAME="AEN4212"
></A
><H2
>Name</H2
>LiapSolve&nbsp;--&nbsp;Computes Nash equilibria via function minimization</DIV
><DIV
CLASS="REFSYNOPSISDIV"
><A
NAME="AEN4215"
></A
><H2
>Synopsis</H2
><TABLE
BORDER="0"
BGCOLOR="#E0E0E0"
WIDTH="100%"
><TR
><TD
><PRE
CLASS="SYNOPSIS"
>LiapSolve[start-&#62;BEHAV, {asNfg-&#62;False}, {stopAfter-&#62;1}, 
          {nTries-&#62;10}, {accuracy-&#62;0.000000}, {time&#60;-&#62;0}, 
          {nEvals&#60;-&#62;0}, {traceFile&#60;-&#62;(Output)}, 
          {traceLevel-&#62;0}] =: LIST(BEHAV)
LiapSolve[start-&#62;MIXED, {stopAfter-&#62;1}, {nTries-&#62;10}, 
          {accuracy-&#62;0.000000}, {time&#60;-&#62;0}, {nEvals&#60;-&#62;0}, 
          {traceFile&#60;-&#62;(Output)}, {traceLevel-&#62;0}] =: LIST(MIXED)</PRE
></TD
></TR
></TABLE
></DIV
><DIV
CLASS="REFSECT1"
><A
NAME="AEN4217"
></A
><H2
>Description</H2
><P
><TT
CLASS="FUNCTION"
>LiapSolve</TT
>
searches for a Nash equilibrium by minimizing a Lyapunov function
which is zero exactly at Nash equilibria.  The algorithm starts from
the initial starting point determined by the parameter 
<TT
CLASS="PARAMETER"
><I
>start</I
></TT
>.
The algorithm is not guaranteed to find a Nash equilibrium from any
fixed starting point.  The algorithm thus incorporates the capability
of restarting.  If a Nash equilibrium is not found, it will keep
searching from new randomly chosen starting points until a Nash
equilibrium has been found or the maximum number of tries (parameter
<TT
CLASS="PARAMETER"
><I
>nTries</I
></TT
>) is exceeded, whichever comes first.  The list of
solutions found is returned.</P
><P
>The behavior of the algorithm may be modified by specifying the following
optional parameters:
<P
></P
><UL
><LI
><P
><TT
CLASS="PARAMETER"
><I
>asNfg</I
></TT
> By default, extensive forms are solved in the extensive form.
By setting this parameter to <TT
CLASS="LITERAL"
>True</TT
>, each marked subgame of the
extensive form is converted to its corresponding reduced normal form game,
solved, and the overall behavior profile reconstructed from these
solutions.</P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>nTries</I
></TT
>: Sets the maximum number of attempts at finding an
equilibrium. Default is 10.</P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>stopAfter</I
></TT
>: Sets the number of equilibria to find.  Default is 1.</P
></LI
><LI
><P
><TT
CLASS="PARAMETER"
><I
>accuracy</I
></TT
>: Resulting solutions are ``epsilon equilibria'' to at least
this accuracy.  I. e., no unilateral deviation by any player will
result in an improvement of more than the accuracy.  Default is
1.0e-8.</P
></LI
></UL
></P
></DIV
><DIV
CLASS="NAVFOOTER"
><HR
ALIGN="LEFT"
WIDTH="100%"><TABLE
WIDTH="100%"
BORDER="0"
CELLPADDING="0"
CELLSPACING="0"
><TR
><TD
WIDTH="33%"
ALIGN="left"
VALIGN="top"
><A
HREF="bif.lessequal.html"
>&#60;&#60;&#60; Previous</A
></TD
><TD
WIDTH="34%"
ALIGN="center"
VALIGN="top"
><A
HREF="gambit.html"
>Home</A
></TD
><TD
WIDTH="33%"
ALIGN="right"
VALIGN="top"
><A
HREF="bif.liapvalue.html"
>Next &#62;&#62;&#62;</A
></TD
></TR
><TR
><TD
WIDTH="33%"
ALIGN="left"
VALIGN="top"
>LessEqual</TD
><TD
WIDTH="34%"
ALIGN="center"
VALIGN="top"
><A
HREF="c2106.html#GCL.BUILTIN"
>Up</A
></TD
><TD
WIDTH="33%"
ALIGN="right"
VALIGN="top"
>LiapValue</TD
></TR
></TABLE
></DIV
></BODY
></HTML
>