Xianwen Shi

Contests for Status

We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A principal determines the number and size of status categories in order to maximize output. We first consider the pure status case without tangible prizes. Our results connect the optimal partition in status categories to properties of the distribution of ability among contestants. The top status category always contains a unique element. For distributions that have an increasing failure rate (IFR), a proliferation of status classes is optimal, whereas the optimal partition involves only two categories if the distribution of abilities is sufficiently concave. Moreover, for IFR distributions, a coarse partition with two status categories achieves at least half of the output obtained in the optimal partition with many categories. Finally, if status is derived solely from monetary rewards, we show that the optimal partition in status classes contains only two categories.

On the Equivalence of Bayesian and Dominant Strategy Implementation

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.

Market Segmentation: The Role of Opaque Travel Agencies

This paper investigates the role of discount travel agencies such as Priceline and Hotwire in the market segmentation of the hotel and airline industries. These agencies conceal important characteristics of the offered services, such as hotel locations or flight schedules. We explicitly model this opaque feature and show that it enables service providers to price discriminate between those customers who are sensitive to service characteristics and those who are not. Service providers can profit from such discrimination despite the fact that the opaque feature virtually erases product differentiation and thus intensifies competition. The reason is that the intensified competition for less sensitive customers enables service providers to commit to a higher price for more sensitive customers, which leads to higher profits overall. This explains why airlines or hotels are willing to lose the advantage of product differentiation and offer services through discount travel agencies.

Optimal Auctions with Information Acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.

Carrots and Sticks: Prizes and Punishments in Contests

We study optimal contest design in situations where the designer can reward high performance agents with positive prizes and punish low performance agents with negative prizes. We link the optimal prize structure to the curvature of distribution of abilities in the population. In particular, we identify conditions under which, even if punishment is costly, punishing the bottom is more effective than rewarding the top in eliciting effort input. If punishment is costless, we study the optimal number of punishments in the contest.

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].

Liquidity Pools, Risk Sharing, and Financial Contagion

This paper reevaluates the Allen–Gale (2000) analysis of interbank deposits to explain financial contagion. This paper modifies the pecking order of asset liquidation developed in Allen–Gale, which is essential in fragility analysis. Furthermore, we also provide a claim structure called “liquidity pool” that can both achieve risk sharing and prevent financial contagion across regions when asymmetric information about bank assets is absent. This model can partly explain why bank panics reduced substantially after the founding of the Fed and the role of IMF in regional financial crises.

Level-k reasoning in a generalized beauty contest☆

We study how the predictive power of level-k models changes as we perturb the classical beauty contest setting along two dimensions: the strength of the coordination motive and the information symmetry. We use a variation of the Morris and Shin (2002) model as the unified framework for our study, and find that the predictive power of level-k models varies considerably along these two dimensions. Level-k models are successful in predicting subject behavior in settings with symmetric information and a strong coordination motive. Their predictive power weakens significantly when either private information is introduced or the importance of the coordination motive is decreased.

Becker Meets Ricardo: Multisector Matching with Social and Cognitive Skills

This paper presents a tractable framework for studying frictionless matching in school, work, and marriage when individuals have heterogeneous social and cognitive skills. In the model, there are gains to specialization and team production, but specialization requires communication and coordination between team members, and individuals with more social skills communicate and coordinate at lower resource cost. The theory delivers full task specialization in the labor and education markets, but incomplete specialization in marriage. It also captures well-known matching patterns in each of these sectors, including the commonly observed many-to-one matches in firms and schools. Equilibrium is equivalent to the solution of an utilitarian social planner solving a linear programming problem.

Academic wages and pyramid schemes: a mathematical model ∗

Abstract This paper analyzes a steady state matching model interrelating the education and labor sectors. In this model, a heterogeneous population of students match with teachers to enhance their cognitive skills. As adults, they then choose to become workers, managers, or teachers, who match in the labor or educational market to earn wages by producing output. We study the competitive equilibrium which results from the steady state requirement that the educational process replicate the same endogenous distribution of cognitive skills among adults in each generation (assuming the same distribution of student skills). We show such an equilibrium can be found by solving an infinite-dimensional linear program and its dual. We analyze the structure of our solutions, and give sufficient conditions for them to be unique. Whether or not the educational matching is positive assortative turns out to depend on convexity of the equilibrium wages as a function of ability, suitably parameterized; we identity conditions which imply this convexity. Moreover, due to the recursive nature of the education market, it is a priori conceivable that a pyramid scheme leads to greater and greater discrepancies in the wages of the most talented teachers at the top of the market. Assuming each teacher teaches N students, and contributes a fraction θ ∈ ] 0 , 1 [ to their cognitive skill, we show a phase transition occurs at N θ = 1 , which determines whether or not the wage gradients of these teachers remain bounded as market size grows, and make a quantitative prediction for their asymptotic behavior in both regimes: N θ ≥ 1 and N θ 1 .