Multi-stage contests: theory and experiments

In a multi-stage contest known as a two-player race, players display two fundamental behaviors: (1) The laggard will make a last stand in order to avoid the cost of losing; and (2) the player who is ahead will defend his lead if it is threatened. Last stand behavior, in particular, contrasts with previous research where the underdog simply gives up. The distinctive results are achieved by introducing losing penalties and discounting into the racing environment. This framework permits the momentum effect, typically ascribed to the winner of early stages, to be more thoroughly examined. I study the likelihood that the underdog will catch up. I find that neck-and-neck races are common when the losing penalty is large relative to the winning prize, while landslide victories occur when the prize is relatively large. Closed-form solutions are given for the case where players have a common winning prize and losing penalty.

Chapter 2 then experimentally examines the prediction of last stand behavior in a multi-battle contest with a winning prize and losing penalty, as well as the contrasting prediction of surrendering in the corresponding contest with no penalty. We find varied evidence in support of these hypotheses in the aggregated data, but more conclusive evidence when scrutinizing individual player behavior. Players tend to adopt one of several strategies. We develop a taxonomy to classify player types and study how the different strategies interact. The last stand and surrendering behaviors have implications for winning margins and the likelihood of an upset, which we investigate. Behaviorally, players are typically more aggressive when they reach a state in the contest by winning rather than by losing.

The third and final chapter is a distinct departure from the study of multi-battle contests. Using comprehensive census data for Cornwall County, England, I create a panel dataset that spans six censuses (1841--1891)—possibly the largest panel dataset for Victorian England at present. I present the methodology for linking individuals and families across these censuses. This methodology incorporates recent advances in census linking (including the use of machine learning) and introduces new methods for tracking migration and changes in household composition. I achieve a forward matching rate of 43%. The additional inclusion of marriage and death records could allow for well over 60% of the population to be accounted for from one census to the next. Using this new panel, I investigate the frequency with which sons pursue the same occupations that they observed their fathers doing while growing up. For sons that did not follow in their father's footsteps, I identify some correlates that may have contributed to the change.