On equilibrium existence in generalized multi-prize nested lottery contests

The generalized multiple-prize nested lottery contest framework has been broadly applied to model noisy competitions that award prizes to multiple recipients. Assuming homogeneous and risk-neutral players, previous studies have typically solved for the symmetric strategy profile that satisfies the first-order condition as the equilibrium solution to the game. The literature has yet to formally establish equilibrium existence because of a technical challenge caused by the presence of multiple prizes. The associated payoff structure dismisses the key property of contests as aggregative games and nullifies the usual approach for equilibrium analysis. We develop an alternative approach to ascertain the property of players' payoff functions without assuming homogeneous and/or risk-neutral players, which enables us to establish equilibrium existence. We then consider a setting that allows for incomplete information and develop an indirect approach to establish equilibrium existence of the Bayesian contest game.