  The deduction game is a variation of the game of cops and robber on graphs in
which searchers must capture an invisible evader in at most one move. Searchers
know each others' initial locations, but can only communicate if they are on
the same vertex. Thus, searchers must deduce other searchers' movement and move
accordingly. We introduce the deduction number and study it for various classes
of graphs. We provide upper bounds for the deduction number of the Cartesian
product of graphs.
