We propose a notion of fairness for allocation problems in which different agents may have different reservation utilities, stemming from different outside options, or property rights. Fairness is usually understood as the absence of envy, but this can be incompatible with reservation utilities. It is possible that Alice's envy of Bob's assignment cannot be remedied without violating Bob's participation constraint. Instead, we seek to rule out justified envy, defined as envy for which a remedy would not violate any agent's participation constraint. We show that fairness, meaning the absence of justified envy, can be achieved together with efficiency and individual rationality. We introduce a competitive equilibrium approach with price-dependent incomes obtaining the desired properties.

我们提出分配问题的公平概念，在这种分配问题中，不同的代理人可能有不同的预订效用，这取决于不同的外部选择权或财产权利。通常将公平理解为缺乏嫉妒，但这可能与预订实用程序不兼容。在不违反Bob的参与约束的情况下，无法纠正Alice对Bob的羡慕之情。取而代之的是，我们试图排除有理由的嫉妒，即被定义为一种嫉妒，而嫉妒的补救措施不会违反任何代理的参与约束。我们表明，公平，意味着没有正当的嫉妒，可以与效率和个人理性一起实现。我们引入竞争均衡方法，使价格相关的收入获得所需的属性。