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First: Whatever the costs and flaws, the lure of big-time sports in public institutions, and the idea of a payoff in applications and prestige for winning teams, seem to be stronger than ever.
Payoffs of politicians still happen, of course.
The payoffs of market creation are huge.
These behaviors can be mapped into a network of incentives where each individual payoff depends on the payoffs of others.
The payoffs of this game will be as follows.
But the payoffs of space programs can justify their expense.
The payoffs of these two parties can be offset by the other players' payoffs.
The payoffs of going into science are pretty uncertain.
In the first period, as X becomes arbitrarily large the payoffs of player 3 dominate the payoffs of player 1.
The average group payoff is now calculated as the average of the payoffs of those group members, who participate in the group competition.
Strict equal-material-payoff-monotonicity requires that more preferred allocations are reached when the payoffs of both agents are increased along the 45° line.
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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