The off-switch game is a game theoretic model of a highly intelligent robot interacting with a human. In the original paper by Hadfield-Menell et al. (2016b), the analysis is not fully game-theoretic as the human is modelled as an irrational player, and the robot's best action is only calculated under unrealistic normality and soft-max assumptions. In this paper, we make the analysis fully game theoretic, by modelling the human as a rational player with a random utility function. As a consequence, we are able to easily calculate the robot's best action for arbitrary belief and irrationality assumptions.
In this paper, we provide a detailed review of previous classifications of $$2\times 2$$
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games and suggest a mathematically simple way to classify the symmetric $$2\times 2$$
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games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a method for using a stereographic projection to create a compact 2-d representation of the game space.
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