Aggregative games with discontinuous payoffs at the origin

Abstract

Recently a framework was developed for aggregative variational inequalities by means of the Selten–Szidarovszky technique. By referring to this framework, a powerful Nash equilibrium uniqueness theorem for sum-aggregative games is derived. Payoff functions are strictly quasi-concave in own strategies but may be discontinuous at the origin. Its power is illustrated by reproducing and generalising in a few lines an equilibrium uniqueness result in Corchón and Torregrosa (2020) for Cournot oligopolies with the Bulow–Pfleiderer price function. Another illustration addresses an asymmetric contest with endogenous valuations in Hirai and Szidarovszky (2013).