Curriculum Vitae
Jun Xiao |
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Curriculum Vitae |
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THESIS ABSTRACT Asymmetric All-Pay Contests with Heterogeneous Prizes (Job Market Paper) This paper studies complete-information all-pay contests in which participants with differing abilities compete for multiple non-identical prizes. The participants have different but linear (that is, constant marginal) costs of performance and the prize sequence is either quadratic (the second-order difference in prizes is a positive constant) or geometric (the ratio of successive prizes is constant). Each player chooses a costly performance level. The player with the highest performance receives the highest prize; the player with the second-highest performance receives the second-highest prize; and so on. A player's payoff is his winnings, if any, minus his cost of performance. Costs are incurred regardless of whether he wins a prize or not. The main result allows us to address some well-known questions regarding contests. I first investigate the issue of tracking students, which in practice, typically entails the placement of students with similar abilities together. In particular, consider a situation in which a school wants to allocate a group of students into different classrooms in order to maximize their total effort. I demonstrate, by means of an example, that tracking is better than not tracking if the returns to the lower-ranked students are not too small whereas tracking is worse than not tracking if the returns to the lower-ranked students are very small. Second, I consider the situation in which a designer of a contest has a fixed amount of prize money and wants to maximize the total performance. I show that winner-takes-all contests may not be optimal once players are asymmetric. Finally, I study the incentive effects of introducing a very efficient player—a superstar—into the contest. Contrary to Brown’s (2011) theoretical result, when existing players are asymmetric, the introduction of a superstar may actually increase the total performance of these players.
Bargaining Order in a Multi-Person Bargaining Game This paper studies a complete-information bargaining game with one buyer and multiple sellers of different "sizes" or bargaining strengths. Examples include the bargaining between a real estate developer and landowners; bargaining between an airline and different labor unions, etc. Which seller should the buyer bargain with first, the one with a large size or the one with a small size? The model in this paper builds on that of Cai (2000) by introducing endogenous bargaining order. In particular, a buyer needs to purchase from multiple sellers in order to reap the value of a project. A seller with a larger size has a higher outside/inside option when bargaining with the buyer. In contrast to the literature, in this model, the buyer determines the bargaining order in the following manner. The buyer chooses a seller and makes an offer to the seller, which the seller can accept or reject. If a price is accepted, the price is paid and the seller leaves the game. If the price is rejected, the seller makes an offer, which the buyer can accept or reject. If a price is accepted or both the buyer’s and the seller’s offers are rejected, the buyer chooses a remaining seller to bargain with in the same fashion. The buyer’s payoff is the value of the project minus the price that she pays; a seller’s payoff is the price he receives and the value of his inside options until his agreement. 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 a unique subgame perfect equilibrium outcome again with the order of increasing size. Finally, if the bargaining ends in finite periods, there is also a unique equilibrium outcome with the same order.
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