I used to think that such positions are typically combinatorial feasts, requiring impressive trees of analysis from each player. But now I think otherwise. It seems to me now that as the players struggle to keep each switch a switch, each switch will almost certainly acquire an air bag, and the presence of air bags will let the remainder of each switch reduce to a single cannibal. In its last gasp a switch will consist of an airbag and one other cannibal - three cannibals in all.
Determining who will win such a struggle, then, is as easy as determining the winner of a routine cannibal war, and the technique is in fact identical. For instance, if two such switches are the only biospheres in a given position, the winner will be the player to move when there are an odd number of cannibals.
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