Posted By Simpson on April 14, 2002 at 06:46:02:
In Reply to: Re: RPS and Nash posted byStu Vessant on April 06, 2002 at 20:53:18:
'Win', 'lose', 'stalemate' aren't strategies, they're outcomes. Simple strategies include 'rock', 'paper', 'scissors' etc., or multi-throw combinations. There are no Nash equilibria in pure strategies in RPS, only mixing equilibria, apart, possibly from the Hagi Naktrah of course.
Simpson
: : Therefore the Nash Equilibrium states that it would be in the best interest of all players to Stalemate.
: : Since this is obviously not the case with RPS the Nash Equilibrium is refuted!
: Ah, not so fast, Dave. You seem to be forgetting here that RPS is a non zero-sum game. There is no "in the best interests of all players", as in a zero-sum game, because only one player may win. Your option "second best [outcome] is to stalemate" is not quite true, as a stalemate is not truly an "outcome". A stalemate simply results in another round being played, until the desired number of wins is obtained. Anyone who can recall the interminable snorefest of the '74 US Nationals (in which average RPMs (rounds per match) was 23) will argue that constant stalemates are in no one's best interests.
: Stu Vessant
: Part-time Operator Developmental Affairs