Turing Completeness and Sid Meier’s Civilization

We prove that three strategy video games from the
Sid Meier’s Civilization
series:
Sid Meier’s Civilization: Beyond Earth
,
Sid Meier’s Civilization V
, and
Sid Meier’s Civilization VI
, are Turing-complete. We achieve this by building three universal Turing machines—one for each game—using only the elements present in the games, and using their internal rules and mechanics as the transition function. We use these machines to prove the undecidability of these games under the unlimited turns, infinite map assumptions; and conclude by providing a sample execution of an algorithm—the three-state Busy Beaver—with one of our machines.