The Complexity of Scotland Yard
Merlijn Sevenster

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.


Keywords: Computational complexity, Scotland Yard, Imperfect information