it is my first post here, sorry in advance if my question is ill-formatted, I did my best.
It's been a while I'm thinking of a modified version of rock-paper-scissor which is assymetrical and wonder what should be the optimal strategy for both players. Basically everything is the same except when player A wins with rock (against scissors), he wins 2 points instead of 1. When player A wins with anything else than rock, he wins 1 point, when player B wins with rock, paper or scissors he wins 1 point. In case of a tie, nobody gains point.
The gains table from player A perspective would be as follow:
| A gain table | A plays Rock | A plays Paper | A plays Scissors |
|---|---|---|---|
| B plays Rock | 0 | 1 | -1 |
| B plays Paper | -1 | 0 | 1 |
| B plays Scissors | 2 | -1 | 0 |
When it is symmetrical between the two players, but with different rewards it is quite easily solved: Optimal Strategy for Rock Paper Scissors with different rewards
I wonder if it is the same here. We have the assumption that both know the strategy of the opponent and adapt their accordingly. What would be the formulas to apply in order to know the mixed strategy of A and B ? Where none wants to change it even by knowing the opponnent's strategy.
Thanks a lot in advance
