Competition in insurance markets can sometimes be harmful. Monopoly can actually provide better coverage for insurance buyers compared to competition. Monopoly can use its market power to offer better deals, while competition leads to poorer performance overall. Cream-skimming behavior in competitive markets prevents firms from helping different risk types. Monopoly retains most of the surplus, but individuals still prefer competitive markets. In simulations, monopoly generally outperforms competition in terms of trade gains for all traders.