Risk Latte - The Hypergame Paradox

Quiz #4
The Hypergame Paradox

“Taken from Mark Rubenstein's web site www.in-the-money.com


A game is called normal if it must terminate in a finite number of moves (for example, tournament chess or tic-tac-toe). The first move of hypergame is to state which normal game is to be played and the remaining moves consist of the moves of the normal game that has been named.

Is hypergame itself a normal game?


  Answer

Suppose hypergame is normal. Since on the first move of hypergame I can choose any normal game, I can say, "let's play hypergame." We are then in the state of hypergame, and it's your move. You can respond, "Let's play hypergame." I can repeat, "Let's play hypergame," and the process can go on indefinitely, contrary to our assumption that hypergame is normal. Therefore, hypergame is not a normal game. Thus, on my first move in hypergame, I cannot choose hypergame; I must choose a normal game. But having chosen a normal game, the game must finally terminate, contrary to the proven fact that hypergame is not normal!



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