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Royal Society Open Science

A quantum Samaritan’s dilemma cellular automaton

Ramón Alonso‐Sanz, Haozhen Situ

Published Jun 1, 2017• 10 citations
Publisher

Abstract

The dynamics of a spatial quantum formulation of the iterated Samaritan's dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.

DOI
10.1098/rsos.160669

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The dynamics of a spatial quantum formulation of the iterated Samaritan's dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.
The dynamics of a spatial quantum formulation of the iterated prisoner's dilemma game is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The evolution is driven by the imitation of the best neighbour. It is shown how spatial structure enables in fully quantum contests a dramatically rapid emergence of mutual cooperation. In unfair contests, such as quantum versus classic players, the velocity in which the quantum players take advantage of its privileged status is also very notable.
Effects of classical/quantum correlations and operations in game theory are analyzed using Samaritan's Dilemma. We observe that introducing either quantum or classical correlations to the game results in the emergence of a unique or multiple Nash equilibria (NE) which do not exist in the original classical game. It is shown that the strategies creating the NE and the amount of payoffs the players receive at these NE's depend on the type of the correlation. We also discuss whether the Samaritan can resolve the dilemma acting unilaterally.