Exact(31)
In particular, I assume that agents are white lie averse: they strictly prefer to tell the truth whenever lying has no effect on their material payoff.
We show how these results extend to a two-dimensional mechanism design setting where the agents have private information about their material payoff types and their reciprocity types.
If voters maximize something else than just their material payoff, then even with correct beliefs about how the world works they may demand bad policies (from the narrow point of view of maximizing income).
The more positive the kindness function is, the higher the material payoff player i is giving to player j and the kinder we would evaluate player i to be.
The more negative the kindness function is, the lower the material payoff player i is giving to player j and the unkinder we would evaluate player i to be.
This suggests that there is more of a material payoff for being thin in the case of White married women than in the case of Black or Hispanic married women.
Similar(29)
The material payoffs of one player in each game are based on X, while the the material payoffs of the other player are based on 1/X.
(pi _{i}:Arightarrow mathbb {R}) are individual i's "material payoffs".
Note that in the outcome that maximizes the sum of the material payoffs when X grows arbitrarily large, players 2 and 3 maximize their own material payoffs, and when indifferent, they maximize their opponents material payoffs, while players 1 and 4 maximize the material payoffs of their opponents.
The first term of the utility function: (pi _{i}) represents the material payoffs of player i.
Also note that if X grows arbitrarily large in game Q(X), the material payoffs of players 2 and 3 dominate their reciprocal payoffs, while the reciprocal payoffs of players 1 and 4 dominate their material payoffs (as no player can change the material payoffs of their partners since they do not play in the same single game).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com