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Dissertation_ChaoYang_041615.pdf (1.64 MB)

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Social Interactions under Incomplete Information: Games, Equilibria, and Expectations

Yang, Chao
http://orcid.org/0000-0002-5516-3128
http://rave.ohiolink.edu/etdc/view?acc_num=osu1429117943

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Economics.
My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter,"A Tobit Model with Social Interactions under Incomplete Information", is an application of the first chapter to censored outcomes, corresponding to the situation when agents' behaviors are subjected to some binding restrictions. In an interesting empirical analysis for property tax rates set by North Carolina municipal governments, it is found that there is a significant positive correlation among near-by municipalities. Additionally, some private information about its own residents is used by a municipal government to predict others' tax rates, which enriches current empirical work about tax competition. The third chapter, "Social Interactions under Incomplete Information with Multiple Equilibria", extends the first chapter by investigating effective estimation methods when the condition for a unique equilibrium may not be satisfied. With multiple equilibria, the previous model is incomplete due to the unobservable equilibrium selection. Neither conventional likelihoods nor moment conditions can be used to estimate parameters without further specifications. Although there are some solutions to this issue in the current literature, they are based on strong assumptions such as agents with the same observable characteristics play the same strategy. This paper relaxes those assumptions and extends the all-solution method used to estimate discrete choice games to a setting with both discrete and continuous choices, bounded and unbounded outcomes, and a general form of incomplete information, where the existence of a pure strategy equilibrium has been an open question for a long time. By the use of differential topology and functional analysis, it is found that when all exogenous characteristics are public information, there are a finite number of equilibria. With privately known exogenous characteristics, the equilbria can be represented by a compact set in a Banach space and be approximated by a finite set. As a result, a finite-state probability mass function can be used to specify a probability measure for equilibrium selection, which completes the model. From Monte Carlo experiments about two types of binary choice models, it is found that assuming equilibrium uniqueness can bring in estimation biases when the true value of interaction intensity is large and there are multiple equilibria in the data generating process.
Lung-fei Lee (Advisor)
Jason Blevins (Committee Member)
Stephen Cosslett (Committee Member)
Lixin Ye (Committee Member)
255 p.
Economics

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Citations

  • Yang, C. (2015). Social Interactions under Incomplete Information: Games, Equilibria, and Expectations [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429117943

    APA Style (7th edition)

  • Yang, Chao. Social Interactions under Incomplete Information: Games, Equilibria, and Expectations. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1429117943.

    MLA Style (8th edition)

  • Yang, Chao. "Social Interactions under Incomplete Information: Games, Equilibria, and Expectations." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429117943

    Chicago Manual of Style (17th edition)

osu1429117943
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