Existence, Uniqueness, and Comparative Statics in Contests

Many important games are aggregative allowing for robust comparative statics analysis even when a game does not exhibit strategic complements or substitutes (Acemoglu and Jensen (2013)). This paper establishes such comparative statics results for contests improving upon existing results by (i) allowing payoff functions to be discontinuous at the origin, and (ii) allowing for asymmetric rent-seeking contests and patent races. A leading example where (i) is relevant is the classical Tullock contest (Tullock (1980)). The paper also studies existence and uniqueness of equilibria extending the results of Szidarovszky and Okuguchi (1997) and Cornes and Hartley (2005) to patent races