[EM] More on ordinal utilities
Mr David Catchpole
s349436 at student.uq.edu.au
Mon Jan 21 20:49:44 PST 2002
Hi, me again on the same subject, which I haven't done much work on
since the last time I sent a message- but possibly enough to realise how
little I know so far about game theory.
I think a good point to start with, if we're trying to work out what
types of games/election methods simply require ordinal
utility/payoffs/rankings, is working out some reliable conditions for
types of games/election methods with perfect information that are
_dependent_ on cardinal utility/payoffs.
One of these conditions, I guess, is that there need to be 3 or more
different action combinations (I'm using Eric Rasmusen, Games and
Information, 3rd Edition, p. 13's definitions, and an "action
combination" is an "ordered set ... of one action for each of the ...
players in the game."). With 2 action combinations, and therefore only 2
payoffs, there's no need for scale when it comes to any player's
comparison of those payoffs.
>From there, I'm trying to work out the conditions, such that, given a
certain game with certain players with certain initial payoffs, there is
some way of changing the payoffs of one of the players, in a way that
doesn't change the order in value of those payoffs, which changes the
Nash equilibrium strategy of that game. Things I'm thinking of are
things like conditions on the number of action combinations with a
non-zero probability in an "initial" mixed Nash equilibrium strategy
(3?).
Does anybody have any ideas on articles, books, etc. that might have the
kind of information I'm looking for? Markus?
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