Essays on the All-Pay Auction

Three all-pay auction models are examined. The first is a symmetric two-player binary-signal all-pay auction with correlated signals and interdependent valuations. The first chapter provides a complete characterization of each form of equilibrium and gives conditions for their existence. The main finding is that there generically exists a unique equilibrium. The unique equilibrium can only be one of four forms of equilibria. I apply my all-pay auction model to elections, where a candidate that receives good news from the polls behaves in a rationally overconfident manner and reduces her equilibrium effort. Consequently, the other candidate can win the election in an upset. The second chapter extends Chapter 1\u27s model to N signals. In comparison, the binary model allows for a guess-verify approach. However, the number of possible guesses increases rapidly when N increases. Hence such an approach is infeasible. Chapter 2\u27s approach is centered around linear algebra techniques and a novel notion of a weakly monotone equilibrium. In a weakly monotone equilibrium the bid supports are ordered by the strong set order but not necessarily separated like the traditional monotone equilibrium. I classify these weakly monotone equilibria into four primary forms. I characterize each form and find sufficient conditions for their existence. Furthermore, for the model used in Rentschler and Turocy (2016), I provide a novel necessary and sufficient condition for the existence of a traditional monotone equilibrium. The third chapter considers a two-stage game: a negotiation stage followed by a conflict stage in case the negotiations break down. In a setting with multi-dimensional correlated types, two players compete over a good that is of uncertain but common value. Conflict is modeled as an all-pay auction, which endogenizes the cost of conflict. In the literature, which assumes independent private values or costs, a peaceful equilibrium, in which war occurs with zero probability need not exist. I find that in my correlated pure common-value model, a peaceful equilibrium always exists and is essentially unique. Further, I show that adding private values to this model worsens the prospect of peace, and conflict might occur