We study a problem inspired by regulated health insurance markets, such as those created by the government in the Affordable Care Act Exchanges or by employers when they contract with private insurers to provide plans for their employees. The market regulator can choose to do nothing, running a Free Market, or can exercise her regulatory power by limiting the entry of providers (decreasing consumer welfare by limiting options, but also decreasing revenue via enhanced competition). We investigate whether limiting entry increases or decreases the utility (welfare minus revenue) of the consumers who purchase from the providers, specifically in settings where the outside option of "purchasing nothing" is prohibitively undesirable. We focus primarily on the case where providers are symmetric. We propose a sufficient condition on the distribution of consumer values for (a) a unique symmetric equilibrium to exist in both markets and (b) utility to be higher with limited entry. (We also establish that these conclusions do not necessarily hold for all distributions, and therefore some condition is necessary.) Our techniques are primarily based on tools from revenue maximization, and in particular Myerson's virtual value theory. We also consider extensions to settings where providers have identical costs for providing plans, and to two providers with an asymmetric distribution.

中文翻译：

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何时限制强制购买下的市场进入

我们研究了受监管健康保险市场启发的问题，例如政府在《平价医疗法案》交易所或雇主与私人保险公司签订合同为其员工提供计划时创建的问题。市场监管者可以选择什么都不做，运行一个自由市场，或者可以通过限制供应商的进入来行使她的监管权力（通过限制选择降低消费者福利，但也通过增强竞争减少收入）。我们调查限制进入是否会增加或减少从供应商处购买的消费者的效用（福利减去收入），特别是在“什么都不买”的外部选项非常不受欢迎的情况下。我们主要关注提供者对称的情况。我们提出了消费者价值分布的充分条件，以便（a）两个市场中都存在独特的对称均衡，以及（b）在有限进入的情况下效用更高。（我们还确定这些结论不一定适用于所有分布，因此某些条件是必要的。）我们的技术主要基于收入最大化的工具，尤其是 Myerson 的虚拟价值理论。我们还考虑扩展到提供商提供计划的成本相同的设置，以及两个不对称分布的提供商。因此某些条件是必要的。）我们的技术主要基于收益最大化的工具，尤其是 Myerson 的虚拟价值理论。我们还考虑扩展到提供商提供计划的成本相同的设置，以及两个不对称分布的提供商。因此某些条件是必要的。）我们的技术主要基于收益最大化的工具，尤其是 Myerson 的虚拟价值理论。我们还考虑扩展到提供商提供计划的成本相同的设置，以及两个不对称分布的提供商。