 The Hypergame paradox is a more recent addition to the list of set-theoretic paradoxes, invented by Zwicker (1987). Let us call a two-player game well-founded if it is bound to terminate in a finite number of moves. Tournament chess is an example of a well-founded game. We now define hypergame to be the game in which player 1 in the first move chooses a well-founded game to be played, and player 2 subsequently makes the first move in the chosen game. All remaining moves are then moves of the chosen game. Hypergame must be a well-founded game, since any play will last exactly one move more than some given well-founded game. However, if hypergame is well-founded then it must be one of the games that can be chosen in the first move of hypergame, that is, player 1 can choose hypergame in the first move. This allows player 2 to choose hypergame in the subsequent move, and the two players can continue choosing hypergame ad infinitum. Thus hypergame cannot be well-founded, contradicting our previous conclusion.