Uncertainty and Fair Expectations

What pay can a worker expect when he is unsure about his ability (or effort supply) and that of his co-workers? Workers have varying (unobserved) abilities, but can observe their distributions in the population. We uncover four findings. First, we uniquely characterize workers' expected pay in a setup that generalizes the model of a neoclassical firm, thanks to a set of axioms that extend classical axioms of fairness under conditions of uncertainty. Second, we introduce the notion of the probabilistic core and show that our characterized pay scheme is stable in quasimodular technological environments —a new class which includes supermodular technologies. Third, we analyze workers' optimizing behaviors in the firm and uncover conditions that guarantee the existence, uniqueness, and efficiency of the Nash equilibrium under our fair pay scheme and costly individual actions. Finally, we develop an application to Cournot oligopoly, finding that our equilibrium coincides with the Cournot equilibrium