  One of the recognized principal issues brought along by the steadfast
migration towards power electronic interfaced energy sources is the loss of
rotational inertia. In conventional power systems, the inertia of the
synchronous machines plays a crucial role in safeguarding against any drastic
variations in frequency by acting as a buffer in the event of large and sudden
power generation-demand imbalances. In future power electronic-based power
systems, the same role can be played by strategically located virtual inertia
devices. However, the question looms large as to how the system operators would
procure and pay for these devices. In this article, we propose a market
mechanism inspired by the ancillary service markets in power supply. We
consider a linear network reduced power system model along with a robust
$\mathcal{H}_2$ performance metric penalizing the worst-case primary control
effort. With a social welfare maximization problem for the system operator as a
benchmark, we construct a market mechanism in which bids are invited from
agents providing virtual inertia, who in turn are compensated via a
Vickrey-Clarke-Groves payment rule. The resulting mechanism ensures truthful
bidding to be the dominant bidding strategy and guarantees non-negative payoffs
for the agents. A three-region case study is considered in simulations, and a
comparison with a regulatory approach to the same problem is presented.
