Essays on Contests and Bargaining

Author:

Xiao, Jun

Graduate Program:

Economics

Degree:

Doctor of Philosophy

Document Type:

Dissertation

Date of Defense:

April 23, 2012

Committee Members:

Vijay Krishna, Dissertation Advisor/Co-Advisor
Edward James Green, Committee Member
Adam Slawski, Committee Member
Kalyan Chatterjee, Special Member

Keywords:

All-Pay Contest
Tracking
Bargaining Order

Abstract:

Chapter 1. Asymmetric All-Pay Contests with Heterogeneous Prizes. This chapter studies complete-information, all-pay contests with asymmetric players competing for multiple heterogeneous prizes. In these contests, each player chooses a performance level or "score". The first prize is awarded to the player with the highest score, the second, less valuable prize to the player with the second--highest score, etc. Players are asymmetric in that they incur different constant costs per-unit of score. The prize sequence is assumed to be either quadratic or geometric. I show that each such contest has a unique Nash equilibrium and exhibit an algorithm to construct the equilibrium. I then apply the main result to study: (a) the issue of tracking students in schools, (b) the incentive effects of "superstars", and (c) the optimality of winner-take-all contests. Chapter 2. Grouping Players in All-Pay Contests. This chapter considers a situation with one designer and students with two types of abilities. The designer has a fixed budget of prize money, and he can assign the students into two classrooms and divide the prize money into prizes for each classroom. The assigned students in each classroom choose their scores to compete for the prizes in an all-pay contest as in Chapter 1. If the unit of prize is small, and if the school has to distinguish different ranks and wants to maximize the total score, it is optimal to group students with similar abilities together. Chapter 3. Bargaining Order in a Multi-Person Bargaining Game. This chapter studies a complete-information bargaining game with one buyer and multiple sellers of different "sizes" or bargaining strengths. The bargaining order is determined by the buyer. If the buyer can commit to a bargaining order, there is a unique subgame perfect equilibrium outcome where the buyer bargains in order of increasing size -- from the smallest to the largest. If the buyer cannot commit to a bargaining order and the sellers are sufficiently different, there is also a unique subgame perfect equilibrium outcome again with the order of increasing size.