Thomas Ferguson and Christian Genest

The University of California at Los Angeles and Université Laval


A many-player constant-sum game of perfect information called "Toetjes", has been investigated by Tomas Feder, Amer Math. Monthly, (1990), in the uniform distribution case. Several players guess in turn what the outcome will be of a random variable, X, with known distribution. Later guesses are made knowing all previous guesses. Then the outcome of X is observed and the player whose guess is closest to X wins. When analyzed as a non-cooperative game, it is seen that the first player to guess has an advantage, and the last player is at a disadvantage. When analyzed as a cooperative game, the last player has the advantage. In a related game, based on the television game, 'The Price is Right', the player closest to but less than X wins; if all guesses are greater than X, the game is player over until there is a winner. In this game, the last player has a strong advantage.