  We design a Copula-based generic randomized truthful mechanism for scheduling
on two unrelated machines with approximation ratio within $[1.5852, 1.58606]$,
offering an improved upper bound for the two-machine case. Moreover, we provide
an upper bound 1.5067711 for the two-machine two-task case, which is almost
tight in view of the lower bound of 1.506 for the scale-free truthful
mechanisms [4]. Of independent interest is the explicit incorporation of the
concept of Copula in the design and analysis of the proposed approximation
algorithm. We hope that techniques like this one will also prove useful in
solving other problems in the future.
