die is rolled three times. After the first
and second roll a player has the option to take the gain equal to the result
of the rolling and end the game or discard the result and continue the game to
the next rolling. At the last rolling the player's gain is the result of the
last rolling. What is the optimal stopping strategy and what is the fair price
for participation in the game?
We introduce the
function
Clearly,
Also,
where the
is the mathematical expectation applied to the variable
.
We
have
Therefore, after the second rolling the player should reject 3,
.
Similarly,
where
Therefore, after the first rolling the player should reject 4,
.
The fair price for the participation in the game is
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