It's true that in a game of chicken there are 2 Nash equilibria that have different EVs for each player. The NEs are Player 1 swerve 0% Player 2 swerve 100% and Player 1 swerve 100% Player 2 swerve 0%. But the game of chicken is not a turn based game. Consider the following pokerfied chicken based toy game, the rules are as follows:
1 street
if the hand reaches showdown, the pot is always split 50:50.
the starting pot is 10bb
effective stacks are 100bb
the only legal bet size is 100bb
rake is 0% for any pot under 150bb
rake is
100% for any pot 150bb or greater.
There are 3 Nash equilibria in this game. They are as follows: (X = check, B = bet, C = call, numbers are the %s)
Code:
p1 EV p1 X p1 B p1 C p2 X p2 B p2 C
0bb 100 0 0 0 100 9.1+
5bb 100 0 9.1+ 100 0 9.1+
10bb 0 100 0+ 0+ 0+ 0
However, only one of these Nash equilibria is stable.
With strategy pair 1, if you change p1's betting % to anything above 0, algorithms designed to find Nash equilibria will not converge back to it. Assume P1 now bets 0.1% say and p2 calls 100%. In the next iteration it may look like 0.05% bet, call 50%. But here the EV of P2's call is more negative than the EV of P1s shove. So it will begin to converge faster to 0. Eventually the shove of p1 will become positive. The same applies to strategy pair 2. The only strategy this doesn't happen for is strategy pair 3, where p1 open shoves always. This is the only stable strategy - any slight change (in fact any change other than assigning 0% or 100% to the values) will always result in it converging back to the strategy.
My guess is that this is the case for poker in general in tournament scenarios. Only 1 will be stable and this will be the one used in real life scenarios and this is the only one that will be found by algorithms searching for NEs.
Games that this is relevant to are tournament games and games with rake. I am hopeful that one day you will allow piosolver to be used for tournament calculations. I think it's worth working on, it would attract many new people to piosolver (it's currently not useful at all for later stages in tournaments). If not then at least I hope you change PioViewer in a way that would allow other engine developers to do this kind of thing.
Last edited by Karganeth; 12-27-2015 at 09:27 PM.