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An analyst wants to study the behavior of players playing a Bayes Nash equilibrium in a game of incomplete information. The analyst can observe some signal sources that the players have, the state of nature, and the actions that the players subsequently choose. The analyst is modest enough to consider it possible that the players might have additional ...

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Would be strange to write it that way. If you had to define something like that, just do the following: Start with a type space $(T,\mu)$ with probability measure $\mu$. Let $\sigma: T \rightarrow \Delta(A)$. Then $\mathbb{P}(a) =\mu(\sigma^{-1}(a))$.

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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 ...

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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 ...

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To answer the first part of your question, we do not need any more assumptions for the comparison of experiments (besides some measurability issues). Before going on, I'll fix some notations to ones that are standard in the game theory literature, and for the sake of my convenience. An experiment (or informtion structure) is defined as a tuple $(S,\pi)$ for ...

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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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To me, Bayesian games are usually "static" in the sense that no "time" is involved. The state is drawn once, and players make decisions, possibly sequentially, and the outcome is determined --- that's the end of the game. On the other hand, stochastic games are "dynamic" in the sense that states are drawn repeatedly, and after ...

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