Asymmetric Contests

We investigate the Nash equilibria of asymmetric, winner-take-all, imperfectly discriminating contests, focusing on existence, uniqueness and rent dissipation. When the contest success function is determined by a production function with decreasing returns for each contestant, equilibria are unique. If marginal product is also bounded, limiting total expenditure is equal to the value of the prize in large contests even if contestants differ. Partial dissipation can occur only when infinite marginal products are permitted. Our analysis relies heavily on the use of ‘share functions’ and we discuss their theory and application. Increasing returns typically introduces multiple equilibria and requires an extension of share functions to correspondences. We describe the appropriate theory and apply it to the characterisation of all equilibria of contests employing the asymmetric generalisation of a widely-used symmetric contest success function.