  We consider a multi-agent delegation mechanism without money. In our model,
given a set of agents, each agent has a fixed number of solutions which is
exogenous to the mechanism, and privately sends a signal, e.g., a subset of
solutions, to the principal. Then, the principal selects a final solution based
on the agents' signals. In stark contrast to single-agent setting by Kleinberg
and Kleinberg (EC'18) with an approximate Bayesian mechanism, we show that
there exists efficient approximate prior-independent mechanisms with both
information and performance gain, thanks to the competitive tension between the
agents. Interestingly, however, the amount of such a compelling power
significantly varies with respect to the information available to the agents,
and the degree of correlation between the principal's and the agent's utility.
Technically, we conduct a comprehensive study on the multi-agent delegation
problem and derive several results on the approximation factors of
Bayesian/prior-independent mechanisms in complete/incomplete information
settings. As a special case of independent interest, we obtain comparative
statics regarding the number of agents which implies the dominance of the
multi-agent setting ($n \ge 2$) over the single-agent setting ($n=1$) in terms
of the principal's utility. We further extend our problem by considering an
examination cost of the mechanism and derive some analogous results in the
complete information setting.
