Doctor of Philosophy
Charles Z. Zheng
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's 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's 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.
Summary for Lay Audience
Every bidder pays their bid in the all-pay auction, but only the highest bidder wins the prize. The fact that everybody pays their bid, a sunk cost, makes the all-pay auction a very appealing theoretical framework to study. There are various real-world competitions where there is this kind of cost. For example, the effort and time in applying for a job are sunk, but only one person gets the job. Countries spend money on their military, but only one country can win the war. All political candidates in an election spend time and money on their campaigns, but only one candidate wins the election.
Because all-pay processes are widespread, it is crucial to solve the mathematical all-pay auction model under reasonable assumptions. The goal of this thesis is to solve the all-pay auction in a general model such that it is applicable to real-world examples.
I use the all-pay auction model to study election campaigns in my thesis. I show that the 2016 US presidential election results might have been caused by rational overconfidence. Clinton, whom the pollsters favored, exhibited a form of complacency which gave her opponent Trump a chance to win the election.
Further, I apply the all-pay auction to military conflict. I provide conditions to avoid war by proposing a peaceful solution.
Schouten, Henk, "Essays on the All-Pay Auction" (2022). Electronic Thesis and Dissertation Repository. 8558.
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