Two Person Games

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0><script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-47423994-1', 'fortunecity.ws'); ga('send', 'pageview'); </script> <center> <br> <div> <script language="javascript" type="text/javascript" src="http://ad.broadcaststation.net/ads/show_ad.php?width=728&height=90"></script> </div> </center> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=90 BGCOLOR="#006699" TEXT="#080000" bgproperties="fixed" background="122285a1erlcgo.gif"> <div> <FONT SIZE="5" COLOR="#FFCC66" FACE="Arial" ><B>The Game Theory in relation to Evolution</B></FONT><B>     |     </B><A HREF="index.htm" TARGET="_top" TITLE="The Game Theory in relation to Evolution"><U><B>home</B></U></A></div> <div>                                                   </div> <div> <B>Back to </B><A HREF="id2.htm" TARGET="_top" TITLE="The Game Theory"><U><B>Nash</B></U></A></div> </td> </tr><tr> <td valign="top" width=210 BGCOLOR="#FFCC66" TEXT="#080000" background="121d2c00dkelyh.gif"> <bR> </td> <td valign="top" height=390 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <I>Two Person Games</I></div> <div> For two person nonzero sum games, the problem of finding Nash equilibria can be formulated as a linear complementarity problem, and exact solutions can be found as long as computations are done in rationals. The <A HREF="id17.htm" TARGET="_top" TITLE="Lcp Algorithm"><U>Lcp algorithm</U></A> solves a two person game using this approach. Note that the Lcp algorithm can also be used directly on an extensive form game, where it implements the Koller, Megiddo, von Stengel Sequence form. To find <I>one</I> Nash equilibrium use Lcp with nEquilib set to 1. </div> <div> For a two person game the <A HREF="id18.htm" TARGET="_top" TITLE="EnumMixed Algorithm"><U>EnumMixed algorithm</U></A> will enumerate all of the extreme points of the components of the set of Nash equilibria, and hence can be used to find <I>all</I> Nash equilibria. Using EnumMixed with nEquilib set to 0 will find all Nash equilibria. To find if there is more than one Nash equilibrium use EnumMixed with nEquilib set to 2.</div> <div>  </div> </td> </tr></table></body>