Value of Persistent Information

We develop a theory of how the value of an agent's information advantage depends on the persistence of information. We focus on strategic situations with strict conflict of interest, formalized as stochastic zero‐sum games where only one of the players observes the state that evolves according to a Markov operator. Operator Q is said to be better for the informed player than operator P if the value of the game under Q is higher than under P regardless of the stage game. We show that this defines a convex partial order on the space of ergodic Markov operators. Our main result is a full characterization of this partial order, intepretable as an ordinal notion of persistence relevant for games. The analysis relies on a novel characterization of the value of a stochastic game with incomplete information.     

A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

Continuity,Inertia, and Strategic Uncertainty: A Test of the Theory of Continuous Time Games

The theory of continuous time games (Simon and Stinchcombe (1989), Bergin and MacLeod (1993)) shows that continuous time interactions can generate very different equilibrium behavior than conventional discrete time interactions. We introduce new laboratory methods that allow us to eliminate natural inertia in subjects' decisions in continuous time experiments, thereby satisfying critical premises of the theory and enabling a first‐time direct test. Applying these new methods to a simple timing game, we find strikingly large gaps in behavior between discrete and continuous time as the theory suggests. Reintroducing natural inertia into these games causes continuous time behavior to collapse to discrete time‐like levels in some settings as predicted by subgame perfect Nash equilibrium. However, contra this prediction, the strength of this effect is fundamentally shaped by the severity of inertia: behavior tends towards discrete time benchmarks as inertia grows large and perfectly continuous time benchmarks as it falls towards zero. We provide evidence that these results are due to changes in the nature of strategic uncertainty as inertia approaches the continuous limit.     

Forced Coexistence and Economic Development: Evidence From Native American Reservations

Studying Native American reservations, and their historical formation, I find that their forced integration of autonomous polities into a system of shared governance had large negative long‐run consequences, even though the affected people were ethnically and linguistically homogenous. Reservations that combined multiple sub‐tribal bands when they were formed are 30% poorer today, even when conditioning on pre‐reservation political traditions. The results hold with tribe fixed effects, identifying only off within‐tribe variation across reservations. I also provide estimates from an instrumental variable strategy based on historical mining rushes that led to exogenously more centralized reservations. Data on the timing of economic divergence and on contemporary political conflict suggest that the primary mechanism runs from persistent social divisions through the quality of local governance to the local economic environment.     

Truthful Equilibria in Dynamic Bayesian Games

This paper characterizes an equilibrium payoff subset for dynamic Bayesian games as discounting vanishes. Monitoring is imperfect, transitions may depend on actions, types may be correlated, and values may be interdependent. The focus is on equilibria in which players report truthfully. The characterization generalizes that for repeated games, reducing the analysis to static Bayesian games with transfers. With independent private values, the restriction to truthful equilibria is without loss, except for the punishment level: if players withhold their information during punishment‐like phases, a folk theorem obtains.     

具有后发优势的不完全信息专利竞赛

先发优势和后发优势会同时存在于专利竞赛中,它们的相对大小将决定两对称企业在专利研发投资时机选择博弈中所产生的均衡类型并影响企业的研发投资决策。考虑不完全信息和技术不确定性,引入信息披露及其滞后效应使得追随者和领导者分别具有后发优势和先发优势,建立实物期权投资决策模型。通过对各最优投资临界信念的计算和分析,结论表明,一定参数条件下,占先博弈和消耗战均有可能发生。信息披露滞后时间越长、技术不确定性程度越低、随机信号到达速度越快、信号质量越高,领导者先发优势就越明显,越易产生占先博弈;反之,追随者后发优势就越明显,越有可能发生消耗战。     

The Farsighted Stable Set

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single‐payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single‐payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single‐payoff and multi‐payoff stable sets, and suggests that they do not coexist.     

Time Horizon and Cooperation in Continuous Time

We study social dilemmas in (quasi‐) continuous‐time experiments, comparing games with different durations and termination rules. We discover a stark qualitative contrast in behavior in continuous time as compared to previously studied behavior in discrete‐time games: cooperation is easier to achieve and sustain with deterministic horizons than with stochastic ones, and end‐game effects emerge, but subjects postpone them with experience. Analysis of individual strategies provides a basis for a simple reinforcement learning model that proves to be consistent with this evidence. An additional treatment lends further support to this explanation.     

Stochastic Learning Dynamics and Speed of Convergence in Population Games

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.     

Program Evaluation and Causal Inference With High‐Dimensional Data

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data‐rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function‐valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced‐form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post‐regularization and post‐selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced‐form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment‐condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function‐valued) parameters within this general framework where any high‐quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high‐dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsity‐based estimation of regression functions for function‐valued outcomes.     

Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff‐relevant consequences as a function of actions. We introduce the notion of a Berk–Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback–Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self‐confirming equilibrium constitute special cases where players have correctly specified models. We provide a learning foundation for Berk–Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.     

IV Quantile Regression for Group‐Level Treatments,With an Application to the Distributional Effects of Trade

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group‐level unobservables, a quantile extension of Hausman and Taylor, 1981. Because of the presence of group‐level unobservables, standard quantile regression techniques are inconsistent in our setting even if the treatment is independent of unobservables. In contrast, our estimation technique is consistent as well as computationally simple, consisting of group‐by‐group quantile regression followed by two‐stage least squares. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic zero‐mean normality of our estimator. As in Hausman and Taylor, 1981, micro‐level covariates can be used as internal instruments for the endogenous group‐level treatment if they satisfy relevance and exogeneity conditions. Our approach applies to a broad range of settings including labor, public finance, industrial organization, urban economics, and development; we illustrate its usefulness with several such examples. Finally, an empirical application of our estimator finds that low‐wage earners in the United States from 1990 to 2007 were significantly more affected by increased Chinese import competition than high‐wage earners.     

Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.     

The Economics of Counterfeiting

We develop a strategic theory of counterfeiting as a multi‐market large game. Bad guys choose whether to counterfeit, and what quality to produce. Opposing them is a continuum of good guys who select a costly verification effort. In equilibrium, counterfeiters produce better quality at higher notes, but verifiers try sufficiently harder that verification still improves. We develop a graphical framework for deducing comparative statics. Passed and counterfeiting rates vanish for low and high notes. Our predictions are consistent with time series and cross‐sectional patterns in a unique data set assembled largely from the Secret Service.     

Bayesian Learning,Smooth Approximate Optimal Behavior,and Convergence to ε‐Nash Equilibrium

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε‐Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non‐probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so‐called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero‐sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.     

Quantile Selection Models With an Application to Understanding Changes in Wage Inequality

We propose a method to correct for sample selection in quantile regression models. Selection is modeled via the cumulative distribution function, or copula, of the percentile error in the outcome equation and the error in the participation decision. Copula parameters are estimated by minimizing a method‐of‐moments criterion. Given these parameter estimates, the percentile levels of the outcome are readjusted to correct for selection, and quantile parameters are estimated by minimizing a rotated “check” function. We apply the method to correct wage percentiles for selection into employment, using data for the UK for the period 1978–2000. We also extend the method to account for the presence of equilibrium effects when performing counterfactual exercises.     

Organizational Integration for Product Development: The Effects on Glitches,On‐Time Execution of Engineering Change Orders,and Market Success

Deviations from requirements during the product development process can be considered as glitches. Fixing glitches, or problems, during the product development process consumes valuable resources, which may adversely affect product development time and hamper the firm's goal to pursue a first‐mover advantage. It is posited that an integrated organizational response can diminish incidences of glitches and improve the ability of the firm to respond to engineering changes, subsequently leading to improved market success. This organizational response frequently includes heavyweight product development managers who are seen as essential catalysts for internal integration. Though internal integration is vital, it is equally important to integrate with customers and suppliers alike because such network partners can provide access to information, knowledge, and unique and complementary resources that are otherwise unavailable to the firm. Findings, which are based on a sample of 191 product development projects in the automotive industry, suggest that some integration routines have a positive impact on product development outcomes and market success, while other routines can in fact hamper the collective effort.     

Tenable Strategy Blocks and Settled Equilibria

When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set‐valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal‐form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal‐form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff‐equivalent equilibrium, a property that other related concepts have not satisfied.