Job Market Signalling of Relative Position, or Becker Married to Spence

We consider a matching model of the labour market where workers that differ in quality send signals to firms that are also vertically differentiated. Signals allow assortative matching in which the highest quality workers send the highest signals and are hired by the best firms. Matching is consider both when wages are fixed (non-transferable utility) and when they are fully flexible (utility is transferable). In both cases payoffs are determined by relative position- the best worker gets the best job. The standard signalling model which communicates the signaller’s absolute type is a special case of the current model of signalling relative position. Furthermore, in the relative model, equilibrium strategies and payoffs depend on the distributions of types of workers and the distribution of firms. This is in contrast with separating equilibria of the standard model which do not respond to changes in supply or demand. Despite incomplete information, equilibrium investment in education by low ability workers can be inefficiently low