Cost-weighted finite search game
= Cost-weighted finite search game
{title2=$v=(c^2+\sum_i c_i^2)/(2c)$}
In a hide-and-search <zero-sum game> with positive inspection costs $c_i$ and $c=\sum_i c_i$, hiding with probabilities $c_i/c$ gives the same expected search cost for every complete search order. For three locations, beginning at $i$ with probability $c_i/c$ and randomizing the remaining two orders also equalizes every hiding location. The common value is the displayed quantity.