Contests with three or more heterogeneous agents

We study monotone equilibrium behavior in contests with observable effort (bid) where three or more participants have distinct risk attitudes and the monetary value for the prize of each is drawn independently from a distinct distribution. These differences can either cause a player to drop out, that is always choose zero effort regardless of his valuation, or use "all-or-nothing" strategies with discontinuous effort choice. Neither complete drop-out nor discontinuous bidding with finitely many gaps is consistent with pure strategy monotone Bayesian-Nash equilibrium in a contest with either ex-ante identical players or only two distinct participants.