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First, $l(\tau)(y)$ is a function of both $\tau$ and $y$, and the dependence on $\tau$ is essential; this is how communication happens. Since $T$ and $Y$ are finite, there is no point in introducing integrals. $\mathbb{E}_{l(\tau)}g(F(y))$ is the expectation over the function when the random value $y$ is distributed according to $l(\tau)$. That is, $$\mathbb{...


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We have that ${\cal I} = ((X^i)_i, \mu)$​ and ${\cal J} = ((Y^i)_i, \nu)$​ are two information structures. An Interpretation mapping for player $i$​​ is a mapping $\phi^i: X^i \to \Delta(Y^i)$​ so it associates with every $x^i$​ a distribution over $Y^i$​. Let $x^i \in X^i$​. Then $\phi^i(x^i)$​ is a distribution over $Y^i$​ so $\phi(x^i)(y^i)$​ is the ...


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