  Vickrey-Clarke-Groves (VCG) mechanisms are often used to allocate tasks to
selfish and rational agents. VCG mechanisms are incentive compatible, direct
mechanisms that are efficient (i.e., maximise social utility) and individually
rational (i.e., agents prefer to join rather than opt out). However, an
important assumption of these mechanisms is that the agents will "always"
successfully complete their allocated tasks. Clearly, this assumption is
unrealistic in many real-world applications, where agents can, and often do,
fail in their endeavours. Moreover, whether an agent is deemed to have failed
may be perceived differently by different agents. Such subjective perceptions
about an agents probability of succeeding at a given task are often captured
and reasoned about using the notion of "trust". Given this background, in this
paper we investigate the design of novel mechanisms that take into account the
trust between agents when allocating tasks.
  Specifically, we develop a new class of mechanisms, called "trust-based
mechanisms", that can take into account multiple subjective measures of the
probability of an agent succeeding at a given task and produce allocations that
maximise social utility, whilst ensuring that no agent obtains a negative
utility. We then show that such mechanisms pose a challenging new combinatorial
optimisation problem (that is NP-complete), devise a novel representation for
solving the problem, and develop an effective integer programming solution
(that can solve instances with about 2x10^5 possible allocations in 40
seconds).
