Comment by partypete

You may be interested in some of the foundational papers exploring game theory models similar to the Ultimatum game[1][2]. These are known as Iterated Prisoner's Dilemmas.

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[1] The Evolution of Cooperation (https://ee.stanford.edu/~hellman/Breakthrough/book/pdfs/axel...)

[2] Evolutionary Dynamics of Spatial Games (https://www.sciencedirect.com/science/article/abs/pii/016727...)