Three-person $n$-stage optimal stopping game where 

players have unequally weighted privilege and 

their purpose is to maximize their own winning 

probability (WP) is  investigated and an explicit 

but informal solution is obtained. 

A distinguishing feature of this game model 

is the fact that players have their own weights 

by which  at each stage player's desired decision 

may be taken away by an opponent  as an outcome of 

drawing a lottery. 

It is shown that even in a game where players are 

``dictator'' and ``subject'', there exists an equilibrium 

strategy-triple by adopting which the ``subject'' improves 

his disadvantage as $n$ increases. For instance, 

in the $\left<\frac{1}{2}, \frac{1}{2}, 0\right>$-weight 

game 0-weight player gets 

$1-2\sqrt 2/3 {\fallingdotseq} 0.0572,$ for $n = 3,$ and 0.122, 

if $n \to \infty.$