Dave Long <dave.long at bluewin.ch> on Wed May 23 14:44:57 PDT 2007

```How about the following:

the Banker (B) is one or more powers-of-magnitude "more powerful"
than the Chumps (C).
each turn, the Banker has the options of coercion, or of fair play.
each turn, the Chump has the options of compliance, or of rebellion.

in the case of fair play, this being a zero-sum game, the best we can
offer is a payoff of zero.
in the case of rebellion, we provide a stochastic game, in which the
chump is (commonly) bankrupted, or (rarely) succeeds in becoming the
new banker.

so the matrix looks like:

C complies       C rebels
B coerces          1,-1                    x,-x
B plays fair        0,0                     1,-1

where x = the chump's stake 90% of the time, and -(the banker's
stake) the other 10% of the time.

I believe that minmax says that the Banker should "play fair" and the
Chumps should "comply".  (If there are only a few chumps, and the
number of rounds is short, the banker can attempt to win a higher
payoff through "coercion" -- but if there are many, the risk becomes
substantial)

-Dave

```