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

From: Galchin Vasili <[email-masked]>
Date: Thu, 6 May 2004 22:29:15 -0700 (PDT)

Hello,

   What relation if any is there
between game semantics and game theory a la von
Neumann/Nash? Also what is relationship between game
theory in model theory and von Neumann/Nash game
theory?

Kind regards, Bill Halchin

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From: Peter McBurney <[email-masked]>
Date: Fri, 07 May 2004 12:32:10 +0100

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.  Players in the latter either just win or lose, or the game is
drawn, at termination; there is no other reward to the players.

Accordingly,  the games of game semantics are closer in spirit and
design to the dialogue games studied and played by philosophers since at
least the time of Aristotle, and which now form the basis for design of
computer interaction protocols.   Presumably the reseach funding
agencies who sponsored Aristotle's research will be pleased that it is,
at long last, being exploited commercially!

Best,

-- Peter McBurney
University of Liverpool

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From: Colin McLarty <[email-masked]>
Date: Mon, 10 May 2004 09:00:52 -0400

At 12:32 07/05/2004 +0100, Peter McBurney <[email-masked]>  wrote:

>this.

That is a nice point. In consequence, so far as I know, no one is
interested in `mixed strategies' for games in set theory or
semantics.  There is no sense to the `average/expected payoff' for a
randomized strategy as there is no payoff.  Mixed strategies are the focus
of most economic and such uses of game theory.  The usual question is how
to find optimal mixed strategies when there is no winning one.

The usual question for games in set theory or semantics is just whether one
player has a winning strategy.  That is the only question in the uses I
know of.