I'm using the open-source game-theory program Gambit (http://gambit.sourceforge.net/
) to solve a simple toy poker game. But Gambit is giving me a solution that does not make sense.
Let me first describe this 2 player game. Each player is a dealt a card 1, 2, or 3 -- 3 being best. Player 1 and Player 2 both have a 1/3 chance of getting any card, and it's possible for both to be dealt the same card (the deal events are independent). Each player antes 2 chips. Player 1 then has the option of raising 1 chip more (making the pot 5 total), or folding. Player 2 can then fold, call, or re-raise (making the pot 7 total). Player 1 can then fold, call, or re-raise again. At that point the raising is over and Player 2 can only call or fold. If both players have the same card at showdown, they split the pot.
Now, if I tell Gambit to solve a linear complementarity system, I get a "rational" solution:
However, if I solve for a solution using a linear program OR using logit trace, I still get something nonsensical:
In particular, the solution still fails to re-raise as Player 1 100% of the time when holding a 3, despite the fact that player 2 will call that raise 50% of the time when holding a 2. Thus, player 1 can still unilaterally improve so I don't see how this can be a NE.
For those wiho have or download gambit, here is that file: