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5

The key is that "since both equilibria satisfy sequential rationality" is no longer true when you consider weak sequential equilibria. Both concepts satisfy sequential rationality on-path, but the whole point of weak equilibria is that off-path, we allow for any beliefs that can disregard sequential rationality, while a PBE would force you to have ...

3

You take $p$ to be the corresponding correlated equilibrium with $A_k$ being the strategy space of player $k$ Conditions 1. and 2. mean that each player can compute the prescribed action they should play and that they do not know more than this prescription would give them. This is exactly what a correlated equilibrium requires (together with optimality, of ...

3

Take the Beer and Quiche Game as an example. Let's verify that the following is a weak PBE: Both types ($S$ and $W$) of player 1 choose beer ($B$); When player 2 sees a beer choice, he believes that player 1 is type $S$ with probability $0.9$, i.e. $\mu_2(S\mid B)=0.9$, and he chooses $R$ in response; In case that player 2 sees a quiche choice ($Q$), he ...

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