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The Ultimatum Game is a famous sequential, two-player game intensely studiedin Game Theory. A proposer can offer a certain fraction of some amount of avaluable good, for example, money. A responder can either accept, in which casethe money is shared accordingly, or reject the offer, in which case the twoplayers receive nothing. While most authors suggest that the fairest split of50 % vs. 50 % would be the equilibrium solution, recently R. Suleiman (Anaspirations-homeostasis theory of interactive decisions (2014)) suggested theGolden Ratio, 0.618, to be the solution and argued that such a partitioningwould be considered fair by both sides. He provided a justification in terms ofan approach termed aspirations-homeostasis theory. The main idea is thatresponders tend to accept the minor fraction of the Golden Ratio because theyfeel that this fraction equals, in comparison to the larger fraction obtainedby the proposer, the ratio of the larger fraction and the whole amount. Here wegive an alternative explanation to that suggested solution, which complementsthe reasoning by Suleiman (2014) and is based on infinite continued fractions.

The Golden Ratio as a proposed solution of the Ultimatum Game: An explanation by continued fractions