Five Essays in Economic Theory

Abstract

The five essays in this thesis study game-theoretic auction models and their application to economic theory. <br /> Chapter 1 analyzes asymmetric all-pay auctions where the bidders' private types are independently drawn out of distinct two-point probability distributions. We characterize the unique equilibrium of the two bidder case. For the n bidder case, we study the all-pay auction with asymmetric random participation. The results are applied to models of information disclosure in contests, endogenous choice of type-probabilities, and competing contests. <br /> Chapter 2 considers a market model with rational firms that know the distributions from which their opponents' qualities are drawn. Firms engage in price competition. Consumers only see the firms' prices and rely on word-of-mouth in order to judge the firms' different qualities. All equilibria of the model are characterized. Different equilibria generate identical payoffs for the firms, but different welfare results. In the unique monotone pricing equilibrium, welfare converges to zero in the number of firms. <br /> Chapter 3 (joint work with Philipp Weinschenk) studies a price competition game in which customers are heterogeneous in the rebates they get from either of two firms. We characterize the transition from competitive pricing (without rebates) over mixed strategy equilibrium (for intermediate rebates) to monopolistic pricing (for larger rebates). In the mixed equilibria, each firm's strategy is a mixture of two distinct strategies: (i) aggressive pricing that can steal away customers from the other firm and (ii) defensive pricing that can only attract customers who get the rebate. <br /> Chapter 4 studies the optimal release of advertising and information in independent private values second-price auctions. The seller costly chooses for each bidder a probability of learning about the auction or of receiving information. Mild but sharp conditions are developed under which the seller allocates his informational efforts among the potential bidders as concentrated as possible. The seller overinvests in advertising if the valuations of the bidders are drawn from a distribution with increasing failure rate. He underinvests if the distribution has decreasing failure rate. The overall level of advertising is higher under distributions that are more dispersed in terms of the excess wealth order. <br /> Chapter 5.analyzes a similar problem of information release as in Chapter 4, yet in a different setting. The bidders' valuations are sums of independent, identically distributed random variables. By sending a costly information package to a bidder, the seller can reveal to the bidder the realization of one of the random variables. Our main focus lies on the case of two bidders and on the situation where the seller can sell his information packages to the bidders. It is shown that, essentially, giving the same number of packages to both bidders is dominated by any other choice of dividing the same number of packages.