[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 

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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