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That is, Socrates on Monday is not the same whole materially as Socrates on Friday, because the sum of material parts belonging to Socrates on Monday is not identical to the sum of material parts on Friday (De toto et parte, 301).
Proposition 3 shows that the outcome where the sum of material payoffs is maximized is a sequential group reciprocity equilibrium as some individuals can greatly help their opponents without incurring a high cost to themselves.
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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.
This result is very optimistic as it concludes that in the outcome where the sum of the material payoffs is being maximized, nobody wants to deviate (even if they can increase their own material payoffs by doing it).
Because players 1 and 4 are maximizing their opponents material payoffs and players 2 and 3 are maximizing their own material payoffs, the group fairness equilibrium of the two-period game is the outcome where the sum of the material payoffs is maximized.
The dynamic facility layout problem (DFLP) is the problem of finding positions of departments on the plant floor for multiple periods (material flows between departments change during the planning horizon) such that departments do not overlap, and the sum of the material handling and rearrangement costs is minimized.
Her father was the sculptor Tony Smith, a close friend of Barnett Newman, and, rather like herself, an artist whose significance exceeds the sum of his material achievements.
The Multi-Floor Layout Problem (MFLP) is the problem of finding the position of each department in a plant floor in a multi-floor building without any overlapping between departments in order to optimize a particular objective function, more commonly the sum of the material handling costs.
Therefore, every player is playing their best response in the outcome that maximizes the sum of the material payoffs.
In Example 2, the outcome where the sum of the material payoffs is maximized is one of the sequential group reciprocity equilibria.
We generalize the circumstances in which the outcome where the sum of the material payoffs is maximized is a sequential group reciprocity equilibrium.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com