I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning Bayesian Nash Equilibrium.
The problem set is shown below:
For question 3, I initially tried to solve the first problem using Mixed Bayesian Nash Equilibrium but that doesn't make sense since both Player 1 and Player 2 have weakly dominated strategies, so why would they mix? Also when I combine the matrices I find no Pure Strategy Bayesian Equilibrium.
Is there something I'm missing here? How would I go about solving this question? Some example's would be very helpful
For question 4, I have no idea where to even start solving this question. I haven't come across any questions or tutorial on how to solve for Bayesian Nash Equilibria when BOTH players have don't know what game they're playing. Any and all help on how I would solve this problem would be greatly appreciated.
I think for problem 3 you are right, the game has only pure equilibria: L,u and R,d. (even if usually equilibria are an odd number so probably I am missing something).
For problem 4, we know that player 2 will never choose L. Thus, the only equilibrium is (R,p), that is player 2 chooses R, and player 1 chooses any probability. Notice that if player 2 chooses R, Player 1 is indifferent, while playing R for player2 is weakly dominant, so this is also an equilibrium.