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?
