We study a sequential elimination contest where contestants (e.g., campaigns) spend resources that are provided by strategic players called backers (e.g., donors). In the unique symmetric equilibrium, backers initially provide small budgets, increasing their contributions only if their contestant wins the preliminary round. If backers are only allowed to provide budgets at the start of the game, as opposed to before each round, spending is higher. When unspent resources are refunded to the backer, total spending is higher than when all resources are sunk costs. We also study an extension of the model with asymmetric players.

This dissertation adds to the current understanding of contests. Contests are a class of games in which players compete for a prize be expending resources. Some portion of the resources expended cannot be recuperated, even in the event of a loss. Each chapter extends standard models to incorporate realistic features such as nonprobabilistic uncertainty, budgets, dynamics, or intermediate outcomes. Chapter 1 introduces ambiguity aversion to the all-pay auction and war of attrition. Increasing ambiguity causes weak types to bid lower and strong types to bid higher, in the all-pay auction. In the war of attrition, ambiguity can uniformly decrease the bids. A revenue ranking for the all-pay auction, war of attrition, and standard sealed bid auctions is provided. These results are consistent with much of the experimental literature. Chapter 2 continues the discussion of ambiguity aversion. The main result is a characterization of the set of increasing equilibria in games like the all-pay auction and war of attrition. Unlike with subjective expected utility, even when beliefs are independent of type, an increasing equilibrium may not exist. Sufficient conditions are provided for such an equilibrium to exist. Chapter 3 models endogenous budgets in sequential elimination contests. Contestants depend on a strategic group of players to provide resources that will be spent in the contest. We analyze the effect of timing and spending rules on aggregate spending. When budgets are not replenished between stages, spending is higher. When v unspent resources are refunded, total spending is higher than when all spending is a sunk costs. Chapter 4 introduces an all-pay auction game with an intermediate outcome between winning and losing. When bids are sufficiently different, the player with the highest bid wins a prize, and the other player receives nothing. When bids are close, the outcome is called a tie, and each player receives an intermediate prize. Ties are common in sports, political competition, and war. Equilibrium is characterized for a set of parameters where the tying region is relatively large. vi

Ambiguity aversion is introduced to a class of commonly applied games including the war of attrition and all‐pay auction. In contrast to subjective expected utility, the all‐pay auction is shown to generate less expected expenditure than the first‐price auction. The war of attrition generates less expected expenditure than the all‐pay auction and second‐price auction. In the all‐pay auction, increasing ambiguity causes low types to bid lower and high types to bid higher. In the war of attrition, ambiguity can decrease the bids for all types.