Games in Minkowski Spacetime
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This paper contributes a new class of games called spacetime games with perfect information. In spacetime games, the agents make decisions at various positions in Minkowski spacetime. Spacetime games can be seen as the least common denominator of strategic games on the one hand, and dynamic games with perfect information on the other hand. Indeed, strategic games correspond to a configuration with only spacelike-separated decisions ("different rooms"). Dynamic games with perfect information, on the other hand, correspond to timelike-separated decisions ("in turn"). We show how to compute the strategic form and reduced strategic form of spacetime games. As a consequence, many existing solution concepts, such as Nash equilibria, rationalizability, individual rationality, etc, apply naturally to spacetime games. We introduce a canonical injection of the class of spacetime games with perfect information into the class of games in extensive form with imperfect information; we provide a counterexample showing that this is a strict superset. This provides a novel interpretation of a large number of games in extensive form with imperfect information in terms of the theory of special relativity, where non-singleton information sets arise from the finite speed of light. This framework can be a useful tool for reasoning in quantum foundations, where it is important whether decisions such as the choice of a measurement axis or the outcome of a measurement are spacelike- or timelike- separated. We look in particular at the special case of the Einstein-Podolsky-Rosen experiment with four decision points, and model a corresponding spacetime game structure.
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