Essays on Contest theory

Subhasish Modak Chowdhury, Purdue University

Abstract

Contests are economic or social interactions in which two or more players expend costly resources in order to win prize(s). The resources expended by players determine their probability of winning a prize. This dissertation investigates theoretical and experimental applications of Contest theory in the areas of Industrial Organization, Public Economics, and Political Economy. The research is organized into four essays. In the first essay we construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature. We characterize the equilibria and show that multiple equilibria might exist even under symmetric prize values. Finally, we introduce and characterize several contests new to the literature. In the second essay we analyze a two-bidder first-price all-pay auction under complete information where the winning payoff is non-monotonic in own bids. We derive the conditions for the existence of pure strategy Nash equilibria and fully characterize the unique mixed strategy Nash equilibrium when the pure strategy equilibria do not exist. Unlike the standard all-pay auction results as in Baye et al (1996) or Siegel (2009), under this non-monotonic payoff structure, the stronger bidder has two distinct mass points in his/her equilibrium mixed strategy and the equilibrium support of the weaker player is not continuous. When the bidders face common value, then in the equilibrium mixed strategy both bidders place mass points at the same point of support. The equilibrium payoff conditions stated in Siegel (2009) do not hold in case of pure strategy Nash equilibria. The third essay experimentally examines behavior in the Colonel Blotto game with asymmetric resources. In this constant-sum game, two players simultaneously allocate their resources across n-battlefields, with the objective of maximizing the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players often use a “guerilla warfare” strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players often employ a “stochastic complete coverage” strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields. Due to the constant-sum nature of the game, we examine behavior under both strangers and partners matching protocols. In the auction treatment, under the strangers protocol, players have significant serial correlation in allocations to a given battlefield across time. Under the partners protocol this correlation is significantly reduced, and disappears for the disadvantaged player. The fourth essay analyzes a multi-winner contest with players distributed equidistantly along the circumference of a circle. Players spend costly effort and a fixed number of adjacent players are selected as winners. We characterize the equilibrium under the general case of symmetric valuation and compare our results with other existing studies. Finally, we characterize the equilibrium under two specific asymmetric value examples. This study incorporates economic networks under a contest framework, explores the basis of endogenous coalition formation in contests and has important implications for contest design.

Degree

Ph.D.

Advisors

Martin, Purdue University.

Subject Area

Economics|Commerce-Business|Economic theory

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