Subject: categories: Re: Naive question: game semantics vs game theory

From: "Robert J. MacG. Dawson" <[email-masked]>
Date: Mon, 10 May 2004 09:16:28 -0300

Peter McBurney wrote:
>
> Bill --
>
> One difference is that von Neumann/Nash games typically assume a payoff
> (a reward or loss) to participants upon termination of the game, whereas
> the abstract games discussed in game semantics usually do not assume
> this.

    Although it seems that three-player generalizations of the latter
type of games may need something more nuanced than just "win" or "lose"
to ensure that there is not a situation in which a player who cannot
himself win may make an arbitrary choice of which other player does so.
One obvious solution is to declare a "winner" and  "loser" [who has to
pay the winner, wash the winner's car, or whatever], and (for
instance,in a Nim-type game) to declare that the player due to play
immediately after the winner is the loser. It is then not a matter of
indifference to any player how the game turns out.

    However, there are wheels within wheels: for in a game that is not
completely trivial [a trivial game would be like Nim with N piles of
size 1, in which there are no bad moves] there is the possibility that
the player who is due to come in second if everybody plays to maximize
their immediate position may choose to "throw" the game, moving to third
place and putting the erstwhile loser into the lead. This would be an
irrational play on its own, but in combination with a pact for the new
leader to throw the game in turn, both conspirators would end up ahead
of their original positions. The question now is - is there honor among
hustlers? Will the original loser renege? Can the pact be enforced?

    This lands us fair and square in the middle of the von Neumann/Nash
kind of game theory.  What if anything this says about generalizations
of game sematics I do not know.

    John H. Conway told me when I was a graduate student that this area was
under active investigation by somebody or other, but I haven't heard of
anything that came of it.

    -Robert Dawson