Increasing penetration of renewable energy generation poses a challenge to power system inertia adequacy. It is vital to provide long-term incentive signals to induce a generation mix with adequate inertia supply. However, existing literature rarely studies inertia incentive mechanisms or considers inertia constraints when making generation investment decisions. Thus, we propose an inertia market to quantify the value of inertia and to remunerate inertia provision. To examine the impacts of the inertia market on generation mix, we then propose a stochastic bilevel generation investment equilibrium model that depicts a multi-leader and multi-follower Stackelberg game. The lower level of the model considers the proposed inertia market, along with the energy, reserve, and capacity markets. The upper level considers multiple profit-maximizing strategic producers, and each producer is able to build gas-fired generators, wind generators, and energy storages. Numerical experiments demonstrate that a generation mix with adequate inertia supply can be induced with the proposed inertia market whereas there can be inertia shortage without the inertia market. Interestingly, considering carbon taxes, it is more cost-competitive to invest in wind resources with virtual inertia facilities than to substitute wind resources by thermal generators. Correspondingly, the introduction of an inertia market does not significantly reduce wind generation shares but boosts virtual inertia facility penetration. Our findings imply a future power system powered by fully decarbonized power resources with adequate inertia.