Abstract: This paper develops a tractable model of dynamic network formation with heterogeneous forward-looking agents. The model bridges the gap between recent Macroeconomic models with exogenous production network and static econometric models of networks formation games. I model network formation as sequence of Bayesian incomplete information games in which the dynamic state dependencies of agents' strategies are Markov. This feature of aggregate state dependence allows me to investigate the role of network externality through a global interaction channel. I characterize the Bayesian Markov Perfect symmetric equilibrium by a set of fixed-point equations in conditional choice probabilities. I motivate this approach by developing a second stage general equilibrium model of production networks in an open economy. This second stage model provides the payoff structure for the network formation and relevant Markov sufficient statistics. I propose a simple two step maximum likelihood estimator and develop its asymptotic properties for a single large network. I apply this model to US input-output data. In counterfactual experiments, I find that network externality is quantitatively important for endogenous network formation. Furthermore, negative network externality provides alternative explanation for network persistence. In an extension, I show how endogenous entry and exit of nodes be can jointly formulated with endogenous network formation.
Abstract: This paper investigates the asset pricing implications of heterogeneous risk-neutral investors who are concerned with model misspecification. Building upon the formulation in Harrison and Kreps (1978), investors differ in their probability models of the economy's underlying processes. They have the same information set and agree to disagree with each other. This paper proposes a tractable robust decision problem with potential analytical applications, as demonstrated in a modified Gordon model and other examples. Investors must balance between his model and the worst-case model when investing. This paper contributes to the literature in the following ways. First, the short sell constraint present in the literature is relaxed, leading to a less inflated theory of asset speculation. We show that short selling does not eliminate the speculative bubble. Second, the pricing kernel is shown to be a weighted average of the likelihood ratio between different model to a benchmark model. The model explains the excess return from risky assets by the uncertainty they present. Investors profit from speculating against the market, which aggregates all investors' valuation of the asset. Thus, a large risk premium to a particular investor can be re-interpreted as a large presence of investors who have different views on the asset. Third, Bayesian learning can eliminate bubble in the long run while different priors drive speculation in the short run. Finally, the relative measure of heterogeneous investors directly impacts the equilibrium price and speculative value of the asset, as demonstrated in a numerical example.
Abstract: This paper develops a new framework for evaluating decentralized digital currencies and blockchain based digital economies using dynamic network formation model developed in Xiao (2020). By jointly formulating the entry and exit problem of nodes, peer to peer network formation, and the economic transactions on the blockchain, I extract the value of the blockchain as the aggregate of network sufficient statistic component of individual value functions. Specifically, the relevant network sufficient statistic component turns out to be the condition out-degree distribution of the network and the size of the network. This insight suggests a reduced form estimation using parametric models of the conditional out-degree distribution of the network. I apply this method to the public blockchain data on Bitcoin and study its relevance in explaining the relative price movements of Bitcoin. Furthermore, I develop a model of adoption in the market of multiple competing blockchain currencies based on valuation functions of each blockchain. I find that uncertainty of future economy payoff plays an important role in the adoption of blockchain currencies.
Abstract: This paper introduces a new strategic network formation game in which agents’ payoffs are additively separable in all hyperedges of a network up to n-cliques. There are three major advantages of using an n-clique separable network formation game: first, the payoff structure enables “hyperedge-by-hyperedge" optimization using backward recursion that greatly simplifies computation and analysis of network formation games; second, the payoff of each hyperedge captures the net externality generated in that clique and this leads to a precise characterization of network externality; third, the game has an associated sheaf representation on an n-simplicial complex that allows for the use of powerful mathematical tools from algebraic topology. I characterize and show the existence of the unique efficient Nash equilibrium associated with the game. In a random utility setting, I also show how the likelihood of a network equilibrium can be factored into the likelihoods of individual stars with a specific correlation structure. This paper also suggests adding the numbers of higher-order cliques to control for network externalities in the dyadic econometric model of network formation.