Abstract: I study the strategic investment decisions of competing venture capitals (VCs) in startups, focusing on the impact of uncertainty on investment and startup dynamism. My framework considers multi-round funding requirements and VC optimization based on current information and projections of future success (M&A or IPO). Using a novel dataset on the “life-cycle” of biotech and software startups, I establish that the data identifies model parameters and propose methods to correct for endogenous and dynamic selection to infer true startup values and VC information. Among several others, I find that (1) biotech investors initially possess more information than software investors but learn slower, reflecting sector-specific business models; (2) uncertainty leads to underfunding of promising startups, causing welfare losses of 22% and 21% in biotech and software, respectively; and (3) “dynamic (positive) information externality” from early stage investors to late stage investors causes the former to invest less, leading to welfare losses of $10 billion in biotech and $3 billion in software. I also explore policies to mitigate these losses. Additionally, I estimate that stricter M&A policies reduce VC returns, significantly decreasing startup funding and exacerbating welfare losses.

Abstract: The word 'overfitting' has ambiguous meaning in different contexts. This paper provides 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 generalizability of the model as desired by the contest host, and fitness-tuning that only improves 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 (possibly) different threshold do not. As the contest reward becomes more unequal, low types overfit more. We also provide empirical evidence to support our theoretical predictions.

Abstract: I consider the problem of a seller repeatedly selling an item to a buyer whose value is private information but is drawn from a known distribution. Previous studies assume that both seller and buyer behave strategically and show that trade may not occur even when there is gain from trade. In this work, I explore a new direction: the buyer is still strategic but the seller simply follows some no-regret learning algorithms based on the action history of the buyer. My focus is on the ability of these algorithms to achieve more efficient outcomes and the associated distributional implications. Specifically, I consider three no-regret learning algorithms: (1) punishment-based algorithm, (2) greedy algorithm, and (3) exponential-weight algorithm. I find that all of the three algorithms lead to higher total welfare compared to when both agents are strategic. Additionally, most of the welfare gain is captured by the buyer under the greedy algorithm but by the seller under the punishment-based algorithm. The welfare distribution is in the middle under the exponential-weight algorithm.

Abstract: This paper studies the algorithmic complexity for computing the pure Nash Equilibrium (PNE) in Tullock Contests. The (potentially homogeneous) elasticity parameter determines whether a contestant’s cost function is convex, concave or neither. Our core finding is that the domains of the elasticity parameter govern the complexity for solving Tullock contents. When no contestant’s elasticity parameter lies between 1 and 2, we can design an efficient algorithm to compute the pure NE. However, when many elasticity parameter values fall within 1 and 2, we prove that determining NE existence is NP-complete. For the intermediate case with a small number of  elasticity parameters within 1 and 2, we design a Fully Polynomial-Time Approximation Scheme (FPTAS) to find an epsilon-PNE when an exact PNE exists. All our algorithms are efficiently implemented for solving large-scale instances, and computational experiments demonstrate their effectiveness even in complex scenarios.