On Mon, Jan 20, 2014 at 09:53:41AM -0800, meekerdb wrote: > > Except in games (like chess) you never have perfect knowledge. The > definition of rationality you cited recognized this by saying you > optimised your *expected* utility. > But you can optimise your > expected utility by acting unpredictably and the only way to be sure > that your action is unpredictable is for it to be random. >
I don't think that was what was intended by using expectation values. It is meant to handle unknowns, such as tomorrows weather, or whether you opponent really is a rational player, or if not, just how irrational they are. In terms of chess, the utility must be some measure that approximates the expected probability of winning the game (eg the difference between the weighted sum of pieces own by either player), as the actual probability is computationally intractable, even given accurate knowledge of how rational the opponent is. I do accept that strategies like sacrificing a queen is a rational act, because the payoff several moves in the future is higher than with other choices, even though the immediate utility is negative. But to make random choices is to disregard any such analysis. I'm not sure we can progress much further until we can come up with a simple formal game that advantages random play, so that we can see whether the agents are actually playing rationally when they do so. None of the usual suspects seem to work for me - eg Iterated Prisoners Dilemma, Minority Game, ... Is there anybody lurking with a game theory background that can suggest an example? -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
