Essays in Economic Theory

My dissertation consists of three chapters analyzing questions in economic theory. My first two chapters study auction design settings with non-standard preferences. My final chapter analyzes a sequential duopoly game where there is incomplete information.;In my first chapter, I analyze auction design in a private value setting where I remove the standard restriction that bidders' preferences are linear in money. Instead, I only assume that bidders' have positive wealth effects and declining marginal utility of money. While most research in auction design restricts bidders' preferences to be quasilinear, there are many economic environments in which this restriction is violated. I show that removing the quasilinearity restriction leads to qualitatively different solutions to the auction design problem whether we are concerned with efficiency or revenue maximization.;On efficiency, I show that probabilistic allocations of the good can Pareto dominate the second price auction; and there is no symmetric mechanism that is both Pareto efficient and dominant-strategy implementable. On revenue, I construct a probability demand mechanism with greater expected revenues than standard auction formats when there are sufficiently many bidders.;In my second chapter, I study auction design in a setting where bidders use rank dependent probability weighting. Auctions are a classical example of an economic environment where agents must make choices under risk. The standard approach for evaluating risky prospects is through expected utility theory, but the work of Kahneman and Tversky shows that agents systematically violate expected utility theory. They propose Cumulative Prospect Theory (CPT) as a positive alternative that is able to capture these violations. In this paper I introduce CPT preferences into the canonical independent private value auction model and show that: (1) CPT can be used to explain anomalies that are inconsistent with the benchmark auctions model; and (2) I can construct a lottery ticket system that outperforms standard auctions when there are many bidders. As in my job market paper, the mechanism I propose involves probabilistic allocations of the good, even though the reason and the environment are quite different.;The sub-certainty effect leads to a deficiency in many standard auction formats. Bidders who value the object relatively highly consider winning the auction to be a probable but not certain event. In CPT, such bidders place relatively low decision weights on the outcome where they win. I show that this impedes the auctioneer's ability to raise revenues.;The auctioneer can alternatively implement a lottery ticket system. CPT bidders will place a relatively high decision weight on winning the lottery. This enhances the auctioneer's ability to raise revenue. I use this intuition to construct a lottery ticket system that has strictly greater expected revenues than any standard auction format when there are sufficiently many bidders.;In my last chapter, I consider the Stackelberg Duopoly where the true state of demand is uncertain to the leader and follower. In particular, I focus on separating equilibria of the game. I show that as the information available to the leader becomes arbitrarily accurate, the leader's output is depressed towards zero and the follower's output approaches the monopoly quantity. This result holds true when both the leader and follower observe a public signal that becomes arbitrarily accurate. We see a contrast in behavior between the Stackelberg game with complete information and the Stackelberg game with incomplete information. I show this result to be robust to observational noise.