Xiaoyun Qiu 邱晓云

Abstract:  We study the design of screening mechanisms subject to competition and manipulation. A social planner has limited resources to allocate to multiple agents using only signals manipulable through unproductive effort. We show that the welfare-maximizing mechanism takes the form of a contest and characterize the optimal contest. We apply our results to two settings: either the planner has one item or a number of items proportional to the number of agents. We show that in both settings, with sufficiently many agents, a winner-takes-all contest is never optimal. In particular, the planner always benefits from randomizing the allocation to some agents. 

Abstract: The word `overfitting' has ambiguous meaning in different contexts. The goal of this paper is to provide a game-theoretic definition of overfitting in a generic machine learning contest, where each contestant can allocate effort among two actions: model development that   improves  quality  of the model as desired by the contest host, and parameter tuning that only improve the model's fitness to the particular task in contest which is not  the contest host's true objective. We establish the existence of a symmetric monotone pure strategy  equilibrium in this competition game. It also provides  a natural definition for overfitting in this strategic context by comparing a player's equilibrium effort allocation to a single-agent benchmark scenario. Under our definition, contestants with types below certain threshold (low types) always overfit, whereas those above a (maybe) different threshold do not. As the contest reward increases, low types overfit more and we provide empirical evidence for this.  We also show that the equilibrium observed in Kaggle competition data is monotone.

Abstract:  The data-driven method used in machine learning might lead to too much parameter tuning, i.e., overfitting, instead of model development. We build a game-theoretical model to incorporate the moral hazard problem in machine learning contests to study contestants' incentives to divide effort between model development and parameter tuning.  The predictions of the model are consistent with two empirical observations using the public data from Kaggle competitions: (1) higher reward increases parameter tuning but not the pool of participants; (2) more competent contestants usually achieve higher ranking and conduct more parameter tuning. Our model is equivalent to a Tullock contest with increasing return to scale and heterogeneous contestants.  Given that Nash equilibrium existence is hard to show, we propose a polynomial time algorithm to check existence of epsilon-Nash equilibrium and output one upon existence.  We provide two measures to study the degree of overfitting.  Within the same game, higher types make more submission in total, but overfit less when normalized by the chance of winning. Comparing to a benchmark model where contestants are restricted to spend the same amount of effort on parameter tuning, we find that adding a submission cost discourages parameter tuning, motivates model development, and improves the identification of high types.

Abstratc: We study how unequal gender norms can serve as a cultural institution to facilitate cooperation in societies facing a survival threat, such as warfare or scarce resources. We provide a game-theoretic model to study male and female incentives in the mating contest. When men face a comparative advantage in eliminating threats to the community, such as hunting animals or fighting in battles, it can create incentives for both men and women to actively pursue unequal gender norms. The model predicts a skewed sex ratio towards men in communities facing a survival threat instead of the one-to-one natural sex ratio.  Using data from the Ethnographic Atlas, we find a positive relationship between a society's dependence on hunting for subsistence and patriarchal gender norms.