PP-2006-18: The Complexity of Scotland Yard

PP-2006-18: Sevenster, Merlijn (2006) The Complexity of Scotland Yard. [Report]

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Abstract

This paper discusses a case study of the board game of Scotland Yard from a computational perspective. Interestingly, Scotland Yard is a genuine "playgame" with imperfect information. For reasons not completely clear to me, games with imperfect information have escaped the interest of researchers in Algorithmic combinatorial game-theory. I show by means of a powerset argument, that Scotland Yard can also be considered a game of perfect information, that is surprisingly similar to the original game - up to isomorphism, that is. Using the powerset analysis, I show that Scotland Yard has PSPACE- complete complexity be it with or without imperfect information. In fact, imperfect information may even simplify matters: if the cops are supposed to be consequently ignorant of Mr. X's whereabouts throughout the game the complexity is 'but' NP-complete.

Item Type: Report
Report Nr: PP-2006-18
Series Name: Prepublication (PP) Series
Year: 2006
Uncontrolled Keywords: Computational complexity, Scotland Yard, Imperfect information
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/193

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