  Iterated bipartite quantum games are implemented in terms of the
discrete-time quantum walk on the line. Our proposal allows for conditional
strategies, as two rational agents make a choice from a restricted set of
two-qubit unitary operations. Several frequently used classical strategies give
rise to families of corresponding quantum strategies. A quantum version of the
Prisoner's Dilemma in which both players use mixed strategies is presented as a
specific example. Since there are now quantum walk physical implementations at
a proof-of principle stage, this connection may represent a step towards the
experimental realization of quantum games.
