We study the welfare structure in two-sided large random matching markets. In the model, each agent has a latent personal score for every agent on the other side of the market and her preferences follow a logit model based on these scores. Under a contiguity condition, we provide a tight description of stable outcomes. First, we identify an intrinsic fitness for each agent that represents her relative competitiveness in the market, independent of the realized stable outcome. The intrinsic fitness values correspond to scaling coefficients needed to make a latent mutual matrix bi-stochastic, where the latent scores can be interpreted as a-priori probabilities of a pair being matched. Second, in every stable (or even approximately stable) matching, the welfare or the ranks of the agents on each side of the market, when scaled by their intrinsic fitness, have an approximately exponential empirical distribution. Moreover, the average welfare of agents on one side of the market is sufficient to determine the average on the other side. Overall, each agent's welfare is determined by a global parameter, her intrinsic fitness, and an extrinsic factor with exponential distribution across the population.

翻译：我们研究双边大规模随机匹配市场中的福利结构。在该模型中，每个代理人对于市场另一侧的每位代理人具有潜在的个体评分，其偏好基于这些评分遵循逻辑模型。在邻接条件下，我们提供了稳定结果的精确描述。首先，我们识别出每个代理人的内在适应度，该适应度代表其在市场中的相对竞争力，与实现的稳定结果无关。内在适应度对应于将潜在互惠矩阵转化为双随机所需的缩放系数，其中潜在评分可解释为配对成功的事前概率。其次，在每个稳定（甚至近似稳定）匹配中，代理人各侧的福利或排名，在按其内在适应度缩放后，具有近似指数的经验分布。此外，市场一侧代理人的平均福利足以确定另一侧的平均福利。总体而言，每个代理人的福利由全局参数、其内在适应度以及一个在人群中呈指数分布的外在因素共同决定。