heterogeneity. In this context, the single-crossing condition is sometimes referred to as the Gans-Smart condition. Use in Mechanism Design In mechanism design, the term single-crossing condition (often referred to as the Spence-Mirrlees property for Michael Spence and James Mirrlees, sometimes as the constant-sign assumption) refers to the requirement that the isoutility curve for agents of different types cross only once. This condition guarantees that the transfer in an incentive-compatible direct mechanism can be pinned down by the transfer of the lowest type. This condition is similar to another condition called strict increasing difference (SID). Formally, suppose the agent has a utility function , the SID says we have . The Spence-Mirrlees Property is characterized by . See also Brouwer fixed-point theorem Notes References Asymmetric information Fixed-point theorems