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This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails.
Specifically, because bk/(n + 1) appears in both terms, a t > 0 means that cooperating players were in neighborhoods with other cooperators more on average than defecting participants were in neighborhoods with cooperators.
In simple words, Shapley value assigns credit among a group of cooperating players.
Note that
This means that cooperating players did not move more than defecting players; they simply moved in a different way.
Cooperating players moved 32.03% of the time, while defecting players moved 30.07% of the time (logistic regression with two-way clustering, p = 0.540).
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In fact the C-Solution reflects the opportunity that players 3 and 4 have of getting a joint utility of 57 not cooperating with player 2. In other words player 2 cannot obtain the utility of 34.66 that assigns to players 3 and 4 a joint utility of 55.32, because they may exclude player 2 from the coalition, getting a joint utility of 57.
This strategy has the same signaling behavior as the other strategies in the population, but defects on cooperative players and cooperates with the defectors.
Consequently, the possible outcomes of the games are four: both players cooperate (CC), first player cooperates while the other defects (CD), first player defects while the second cooperates (DC), both players defect (DD).
The characteristic set, V ( A ), is interpreted as the set of achievable outcomes the players in A can guarantee themselves without cooperating with the players in K ∖ A. In particular, an NTU-game G = ( K, V ) is called a TU game when the characteristic set for each coalition A takes the form V ( A ) = x ∈ R | A | : ∑ k ∈ A x k ≤ ν A, (1).
If these N players do not cooperate, then each players' strategy set may vary with other players' strategies, that is, the ith player's strategy set varies with the other players' strategies (x_{-i}).
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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
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