Catch-22 and king-of-the-mountain games: Cycling, frustration, and power

In his classic novel, Catch-22 (1961), Joseph Heller describes a thoroughly frustrating situation faced by a combat pilot in World War II. This is generalized to a 'generic' 2 X 2 strict ordinal game, which subsumes 12 specific catch-22 games. These games, along with 4 king-of-the-mountain games, turn out to be the only games in which moving power is effective, based on the 'theory of moves': each player can induce a better outcome when it possesses this power than when its opponent possesses it. These 16 games constitute 28% of the 57 2 X 2 conflict games, in which there is no mutually best outcome. A specific catch-22 game is used to model the conflict between the pilot and the doctor who can certify his sanity in the Heller novel; a different catch-22 game is used to model medieval witch trials. King-of-the-mountain games portray related situations in which there is a contest to come out on top, but the player who 'loses' does not suffer as much as in a catch-22 game. In all these games, cycling is always possible and frequently observed, despite the presence of pure-strategy Nash equilibria in 10 of the 16 games.