# TOETJES NA

### Thomas Ferguson and Christian Genest

#### The University of California at Los Angeles and
Université Laval

#### Abstract

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.