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I am reading one paper by [Maskin et al. 1979] and cannot figure out some notations. Specially, they defined some states of nature $A$, and each player in the player set $I$ has some preferences over the states of nature. The preference is just some logical orderings of $A$. For example, let $A = \{a, b\}, I = \{1, 2, 3\}$. Let each player $i$ have two preferences $R_i, R_i^{'}$, i.e. $R_1 = [a, b], R_1^{'} = [b, a], \cdots, R_3 =[a, b], R_3^{'} = [b, a]$.

Then the paper uses some notations $a R_i b$, $a P_i b$, and $a I_i b$ without introducing the meaning of these notations. I guess that the meaning of $a R_i b$ is that $a$ is higher/preferred than $b$ in the logical ordering represented by $R_i$. But what do $P$ and $I$ mean here? Are they some terminologies in the Economic literature, or are they related to this specific paper? Unfortunately, I could not find any formal definition of these $a R_i b$, $a P_i b$, and $a I_i b$ in the paper... The paper also talks about Pareto efficiency, I am wondering could this $P$ be related to Pareto efficiency? But I have no idea about what does it mean here with a subscript $P_i$ and with respect to these two states of nature.

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    $\begingroup$ That would be Dasgupta et al, if writing complete references is too much work. $\endgroup$ Mar 3, 2022 at 19:22

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$R,P,I$ are preference orderings. Perhaps you have seen the notation $\succeq$ for preference orderings?

To say $a R_i b$ means $a$ is at least as good as $b$. ($a \succeq b$)

$a P_i b$ means $a$ is strictly preferred to $b$. ($a \succ b$)

$a I_i b$ means $a$ and $b$ are indifferent to one another ($a \sim b$)

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