Efficient Competition Through Cheap Talk: The Case of Competing Auctions

We consider a large market where auctioneers with private reservation values compete for bidders by announcing cheap‐talk messages. If auctioneers run efficient first‐price auctions, then there always exists an equilibrium in which each auctioneer truthfully reveals her type. The equilibrium is constrained efficient, assigning more bidders to auctioneers with larger gains from trade. The choice of the trading mechanism is crucial for the result. Most notably, the use of second‐price auctions (equivalently, ex post bidding) leads to the nonexistence of any informative equilibrium. We examine the robustness of our finding in various dimensions, including finite markets and equilibrium selection.     

Efficient Use of Information and Social Value of Information

This paper analyzes equilibrium and welfare for a tractable class of economies (games) that have externalities, strategic complementarity or substitutability, and heterogeneous information. First, we characterize the equilibrium use of information: complementarity heightens the sensitivity of equilibrium actions to public information, raising aggregate volatility, whereas substitutability heightens the sensitivity to private information, raising cross‐sectional dispersion. Next, we define and characterize an efficiency benchmark designed to address whether the equilibrium use of information is optimal from a social perspective; the efficient use of information reflects the social value of aligning choices across agents. Finally, we examine the comparative statics of equilibrium welfare with respect to the information structure; the social value of information is best understood by classifying economies according to the inefficiency, if any, in the equilibrium use of information. We conclude with a few applications, including production externalities, beauty contests, business cycles, and large Cournot and Bertrand games.     

Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.     

Macroeconomic Implications of Agglomeration

Cities exist because of the productivity gains that arise from clustering production and workers, a process called agglomeration. How important is agglomeration for aggregate growth? This paper constructs a dynamic stochastic general equilibrium model of cities and uses it to estimate the effect of local agglomeration on aggregate growth. We combine aggregate time‐series and city‐level panel data to estimate the model's parameters via generalized method of moments. The estimates imply a statistically and economically significant impact of local agglomeration on the growth rate of per capita consumption, raising it by about 10%.     

The Economics of Density: Evidence From the Berlin Wall

This paper develops a quantitative model of internal city structure that features agglomeration and dispersion forces and an arbitrary number of heterogeneous city blocks. The model remains tractable and amenable to empirical analysis because of stochastic shocks to commuting decisions, which yield a gravity equation for commuting flows. To structurally estimate agglomeration and dispersion forces, we use data on thousands of city blocks in Berlin for 1936, 1986, and 2006 and exogenous variation from the city's division and reunification. We estimate substantial and highly localized production and residential externalities. We show that the model with the estimated agglomeration parameters can account both qualitatively and quantitatively for the observed changes in city structure. We show how our quantitative framework can be used to undertake counterfactuals for changes in the organization of economic activity within cities in response, for example, to changes in the transport network.     

Optimization and equilibrium problems with equilibrium constraints

This paper concerns optimization and equilibrium problems with the so-called equilibrium constraints mathematical programs with equilibrium constraint (MPEC) and equilibrium problems with equilibrium constraint (EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special classes of MPECs and EPECs important in applications.     

Strategic Experimentation with Exponential Bandits

We analyze a game of strategic experimentation with two‐armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free‐riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut‐off strategies. Equilibria where players switch finitely often between experimenting and free‐riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms.     

A Quantitative Theory of Unsecured Consumer Credit with Risk of Default

We study, theoretically and quantitatively, the general equilibrium of an economy in which households smooth consumption by means of both a riskless asset and unsecured loans with the option to default. The default option resembles a bankruptcy filing under Chapter 7 of the U.S. Bankruptcy Code. Competitive financial intermediaries offer a menu of loan sizes and interest rates wherein each loan makes zero profits. We prove the existence of a steady‐state equilibrium and characterize the circumstances under which a household defaults on its loans. We show that our model accounts for the main statistics regarding bankruptcy and unsecured credit while matching key macroeconomic aggregates, and the earnings and wealth distributions. We use this model to address the implications of a recent policy change that introduces a form of “means testing” for households contemplating a Chapter 7 bankruptcy filing. We find that this policy change yields large welfare gains.     

ON‐THE‐JOB SEARCH AND MORAL HAZARD

We analyze the interaction between intertemporal incentive contracts and search frictions associated with on‐the‐job search. In our model, agency problems call for wage contracts with deferred compensation. At the same time workers do on‐the‐job search. Deferred compensation improves workers' incentives to exert effort but distorts their on‐the‐job search decisions. We show that deferred compensation is less attractive when the value to the worker–firm pair of on‐the‐job search is high. Moreover, the interplay between search frictions and wage contracts creates feedback effects. If firms in equilibrium use contracts with deferred compensation, fewer firms with vacancies enter the on‐the‐job search market, and this in turn reduces the distortions created by deferred compensation. These feedback effects between the incentive contracts used and the activity level in the search markets can lead to multiple equilibria: a low‐turnover equilibrium where firms use deferred compensation, and a high‐turnover equilibrium where they do not. Furthermore, the model predicts that firms are more likely to use deferred compensation when search frictions are high and when the gains from on‐the‐job search are small.     

Certifiable Pre‐Play Communication: Full Disclosure

This article asks when communication with certifiable information leads to complete information revelation. We consider Bayesian games augmented by a pre‐play communication phase in which announcements are made publicly. We first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). Next, we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure. This characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in games with strategic complementarities, voting with deliberation, and persuasion games with multidimensional types.     

Nonparametric Identification and Estimation of Nonadditive Hedonic Models

This paper studies the identification and estimation of preferences and technologies in equilibrium hedonic models. In it, we identify nonparametric structural relationships with nonadditive heterogeneity. We determine what features of hedonic models can be identified from equilibrium observations in a single market under weak assumptions about the available information. We then consider use of additional information about structural functions and heterogeneity distributions. Separability conditions facilitate identification of consumer marginal utility and firm marginal product functions. We also consider how identification is facilitated using multimarket data.     

增价拍卖中投标者跳跃报价的收益效应研究

跳跃投标是增价拍卖一种普遍现象,而跳跃投标是否会带来投标方的期望收益的增加是一个值得关注的问题。通过运用博弈论方法,分别寻找单物品和多物品拍卖两种情形下的跳跃报价均衡,计算出跳跃报价均衡下的投标方期望收益,并将其结果与非跳跃报价情形进行比较,给出了投标方希望通过跳跃出价改善其期望收益的一般条件。     

Bargaining within the Supply Chain and Its Implications in an Industry

Our main objective is to investigate the influence of the bargaining power within a chain on its industry. As a building block, we first discuss the implications of bargaining within a single chain by considering an asymmetric Nash bargaining over the wholesale price (BW). We show that both Manufacturer Stackelberg (MS) and vertical integration (VI) strategies are special cases of the BW contract. We then develop the Nash equilibrium in an industry with two supply chains that use BW. We identify the profit‐maximizing (coordinating) bargaining power within this industry. We show that when a chain is not monopolistic, VI does not coordinate the chain and that the MS contract, where the manufacturer has all the bargaining power, is coordinating when competition is intense. We find that the main determinant of the equilibrium in mature industries is to respond well to the actions of the competing chain rather than to directly maximize the profit of each chain. That is, the equilibrium does not necessarily maximize the profit of the entire industry. While a coordination of the industry could then increase the profitability of both chains, such a coordination is likely against antitrust law. Moreover, if one chain cannot change its actions, the other chain may unilaterally improve its profitability by deviating from the equilibrium. Our results lead to several predictions supported by empirical findings, such as that in competitive industries chains will work “close to” the MS contract.     

Sales Force and Competition in Financial Product Markets: The Case of Mexico's Social Security Privatization

This paper examines how sales force impacts competition and equilibrium prices in the context of a privatized pension market. We use detailed administrative data on fund manager choices and worker characteristics at the inception of Mexico's privatized social security system, where fund managers had to set prices (management fees) at the national level, but could select sales force levels by local geographic areas. We develop and estimate a model of fund manager choice where sales force can increase or decrease customer price sensitivity. We find exposure to sales force lowered price sensitivity, leading to inelastic demand and high equilibrium fees. We simulate oft proposed policy solutions: a supply‐side policy with a competitive government player and a demand‐side policy that increases price elasticity. We find that demand‐side policies are necessary to foster competition in social safety net markets with large segments of inelastic consumers.     

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.     

Modeling Interdependent Risks

In an interdependent world the risks faced by any one agent depend not only on its choices but also on those of all others. Expectations about others' choices will influence investments in risk management and the outcome can be suboptimal for everyone. We model this as the Nash equilibrium of a game and give conditions for such a suboptimal equilibrium to be tipped to an optimal one. We also characterize the smallest coalition to tip an equilibrium, the minimum critical coalition, and show that this is also the cheapest critical coalition, so that there is no less expensive way to move the system from the suboptimal to the optimal equilibrium. We illustrate these results by reference to airline security and the control of infectious diseases via vaccination.     

If You're so Smart,why Aren't You Rich? Belief Selection in Complete and Incomplete Markets

This paper provides an analysis of the asymptotic properties of Pareto optimal consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular, we investigate the market selection hypothesis that markets favor traders with more accurate beliefs. We show that in any Pareto‐optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Whereas equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of their parameter space. Finally, we show that in economies with incomplete markets, these conclusions may not hold. With incomplete markets, payoff functions can matter for long‐run survival, and the market selection hypothesis fails.     

团队生产动态博弈

本文建立了团队生产动态(微分 )博弈模型,用Pontryagin最大值原理和共轭点理论研究了该微分博弈的Nash均衡存在的充分必要条件。我们也讨论协调个人理性和集体理性的促进团队合作博弈的机制设置问题。     

Price and Service Competition in an Outsourced Supply Chain

We consider a buyer who outsources the manufacturing of a product to multiple symmetric make‐to‐stock suppliers who compete on price and service (fill rate). The buyer allocates demand to the suppliers using a score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his costs, while the suppliers choose their prices and fill rates to maximize their profits. For the case of dual‐sourcing, we characterize the optimal parameter of the exponential score function, considering the impact of the buyer's decisions on the suppliers, and considering how the suppliers compete against each other to earn a portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then consider a general number of suppliers and show that the equilibrium prices and fill rates, and the buyer's cost, are increasing in the number of suppliers. We compare these results to a model of single‐sourcing, in which the buyer is the Stackelberg leader and extracts all profits from the supplier. We find that the buyer always prefers single‐sourcing to multisourcing. Finally, we study a centralized system and use the results to develop a coordinating contract for the decentralized system.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.