Fictitious play for multi-player games

[jukofyork]

If fictitious play is used to compute a NE in a multi-player game where it is possible for a player to "spite" another (such as in SNGs), then is it correct to assume that each player will attempt to only rationally maximise their own EV for the update rule?

This would mean that you would roughly use this update algorithm:

1. Init strategy to something arbitrary (A).
2. Find the maximal exploitative strategy to A (B).
3. Find the maximal exploitative strategy to a player who plays A or B each with a 50% chance of being selected (C).
4. Find the maximal exploitative strategy to a player who plays A or B or C each with a 33.3% chance of being selected (D).
5. Find the maximal exploitative strategy to a player who plays A or B or C or D each with a 25% chance of being selected (E).
.
.
.
N. Stop when no further exploitative strategy can be found against the strategy collection (or until some reasonable exploitative EV threshold is reached).

This is the basic idea that the ICM Nash Calculator is using.

But, by just assuming that each player will attempt to rationally maximise their own EV seems to ignore the fact that they could also gain EV by another method: You could give up some of your own EV to cost an opponent even more which in turn would force the opponent to change their strategy possibly meaning that you gain EV by threatening to give up some (ie: by partially minimizing your opponent's EV).

This seems to fly in the face of what I know about NE states though, as it shouldn't be possible for a player to deviate profitably from a NE (assuming the above algorithm really does converge to a NE).

Is the reasoning flawed here somewhere? If so, can you think of a simple game as an example?

Is the above algorithm flawed? If so, then what alteration would be required for the update rule?


This post is related to a post in the STT forum which discusses taking a -EV play now to force your opponent to alter his strategy so as to possibly gain more EV in the future. The reason this might be correct is that the play only costs you ~$30, yet costs your opponent ~$300:

http://forumserver.twoplustwo.com/sh...age=0&vc=1

This led me to wondering what is the correct method to compute a NE where it's possible to "spite" an opponent like this:

http://forumserver.twoplustwo.com/sh...age=0&vc=1

Juk [img]/images/graemlins/smile.gif[/img]