Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

Pre-play communication in procurement auctions: Silence is not golden

I study the effect of cheap talk between bidders on the outcome of a first-price procurement auction in which participation is costly. Although no side payments or commitments are allowed, there exists a family of equilibria in which sellers use communication to collude on a subset of participants and/or reveal information about their cost. Cheap talk matters in the sense that it strictly enlarges the set of Nash equilibria (symmetric and asymmetric) and the set of public correlated equilibria of the game. I show that the buyer may benefit from cheap talk between sellers and that the surplus increases in the amount of information revealed in equilibrium under one fairly general condition. This is because when communication is cheap, sellers cannot directly collude on higher prices. Rather, communication leads to competition between fewer, but more aggressive bidders, which entails greater allocative efficiency and a decrease in the total wasteful entry cost.     

Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.     

Dominance solvability of second-price auctions with differential information

We study a class of common-value second-price auctions with differential and finite information. This class is characterized by the property that each bidder’s information set is connected with respect to the common value. We show that the entire class is dominance solvable, and that there is a natural single-valued selection from the resulting set of sophisticated equilibria. Additionally, it is shown that bidder’s information advantage over other bidders is rewarded in sophisticated equilibria.     

Consumer Cognition and Pricing in the Nines in Oligopolistic Markets

The paper fully characterizes the Bertrand equilibria of oligopolistic markets where consumers may ignore the last (i.e., the right-most) digits of prices. Consumers, in this model, do not do this reflexively or out of irrationality, but only when they expect the time cost of acquiring full cognizance of the exact price to exceed the expected loss caused by the slightly erroneous amounts that are likely to be purchased or the slightly higher price that may be paid by virtue of ignoring the information concerning the last digits of prices. It is shown that in this setting there will always exist firms that set prices that end in nine though there may also be some (nonstrict) equilibria where a non-nine price ending occurs. It is shown that all firms earn positive profits even in Bertrand equilibria. The model helps us understand in what kinds of markets we are most likely to encounter pricing in the nines.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

Oligopoly, Financial Structure, and Resolution of Uncertainty

We characterize equilibria of a multistage game in which competing duopolists may acquire and share information in advance of choosing their financial structure which, in turn, precedes production. Given sufficient uncertainty, equilibria exist in which the efficiency and, possibly, coordination gains to acquiring and sharing perfect information are sufficient to break Brander and Lewis's (1986) result wherein both firms issue debt to their mutual disadvantage. However, more interesting may be the robustness of that result when uncertainty is low or when information is imperfect. The key insight is that the consequences of issuing debt are invariant to the level of uncertainty, given that firms can recalibrate the terms of debt to achieve the Stackelberg solution.     

Equilibrium selection in games: the mollifier method

This paper introduces an embedding of a Nash equilibrium into a sequence of perturbed games, which achieves continuous differentiability of best responses by mollifying them over a continuously differentiable density with compact support (window size). Along any sequence with shrinking window size, the equilibria are single-valued whenever the function has a regular Jacobian and the set of equilibria where it is singular has measure zero. We achieve a further reduction of the equilibrium set by inserting within the embedding a procedure that eliminates the strict interior of equilibrium sets. The mollifier can be approximated consistently using kernel density regression, and we sketch a non-stationary stochastic optimization algorithm that uses this approximation and converges with probability one to an equilibrium of the original game.     

上市公司非标准审计意见市场反应的差异性研究

文章以我国证券市场2005年和2006年获得非标准审计意见的上市公司为样本,运用事件研究法和多元回归分析模型,分年度考察了不同类型非标准审计意见的市场反应的差异.研究发现:我国证券市场能够识别持续经营审计意见和非持续经营审计意见之间的差异,但不能识别带强调事项段无保留意见和保留意见、无法表示意见之间的差异;2005年和2006年不同类型非标准审计意见的市场反应存在显著差异.     

论财务治理相关者与财务舞弊

公司财务治理相关者与财务舞弊之间存在着密切关系。本文首先分析管理层、董事会、监事会、注册会计师等公司财务治理相关者与财务舞弊的关系,然后提出通过改变财务信息的生成方式、完善董事会结构、强化监事会功能、变革审计收费体制等措施来防范财务舞弊。     

Die Theorie globaler Spiele: Private Information als Mittel zur Vermeidung multipler Gleichgewichte

Investment decisions with network effects, refinancing illiquid firms, and speculative attacks are typical examples for coordination games with multiple equilibria. By introducing private information about payoff relevant parameters, the theory of global games embeds such coordination games in a stochastic environment, in which the game may have a unique equilibrium. This paper provides an introduction to the theory of global games and shows that it delivers a unique equilibrium if private information is sufficiently precise, while public information may lead to equilibria with self-fulfilling beliefs. This implies some criteria for optimal mechanisms of information dissemination. For example, a well-informed central bank can minimize the prior probability of currency crises by committing to provide information to private actors with small idiosyncratic errors.     

Equilibrium in incomplete markets: I : A basic model of generic existence

This paper demonstrates the generic existence of general equilibria in incomplete markets. Our economy is a model of two periods, with uncertainty over the state of nature to be revealed in the second period. Securities are claims to commodity bundles in the second period that are contingent on the state of nature, and are insufficient in number to span all state contingent claims to value, regardless of the announced spot commodity prices. Under smooth preference assumptions, equilibria exist except for an exceptional set of endowments and securities, a closed set of measure zero. The paper includes partial results for fixed securities, showing the existence of equilibria except for an exceptional set of endowments.     

Strategic analysis of petty corruption with an intermediary

This note reports part of a larger study of “petty corruption“ by government bureaucrats in the process of approving new business projects. Each bureaucrat may demand a bribe as a condition of approval. Entrepreneurs use the services of an intermediary who, for a fee, undertakes to obtain all of the required approvals. In a dynamic game model we investigate (1) the multiplicity of equilibria, (2) the equilibria that are “socially efficient”, and (3) the equilibria that maximize the total expected bureaucrats’ bribe income. We compare these results with those for the case in which entrepreneurs apply directly to the bureaucrats.     

Piracy and Competition

The effects of (private, small-scale) piracy on the pricing behavior of producers of information goods are studied within a unified model of vertical differentiation. Although information goods are assumed to be perfectly differentiated, demands are interdependent because the copying technology exhibits increasing returns to scale. We characterize the Bertrand–Nash equilibria in a duopoly. Comparing equilibrium prices to the prices set by a multiproduct monopolist, we show that competition drives prices up and may lead to price dispersion. Competition reduces total surplus in the short run but provides higher incentives to create in the long run.     

Optimal coordination mechanisms in generalized principal–agent problems

The general principal–agent problem is formulated, in which agents have both private information and private decisions, unobservable to the principal. It is shown that the principal can restrict himself to incentive-compatible direct coordination mechanisms, in which agents report their information to the principal, who then recommends to them decisions forming a correlated equilibrium. In the finite case, optimal coordination mechanisms can be found by linear programming. Some basic issues relating to systems with many principals are also discussed. Non-cooperative equilibria between interacting principals do not necessarily exist, so quasi-equilibria are defined and shown to exist.     

Symmetry and continuity properties of Lindahl equilibria

In this paper it is shown that: (1) some non-symmetric Lindahl equilibria may exist; (2) under usual assumptions, the set of symmetric Lindahl equilibria is non-empty; (3) however, the correspondence which associates with every economy the set of symmetric Lindahl equilibria is not a closed correspondence; (4) there are economies with a measure space of economic agents in which every Lindahl equilibrium is discontinuous.     

Full Nash implementation of neutral social functions

This paper characterizes neutral social functions that are fully implementable. A neutral social function must be monotonic and simple to be fully implementable under either the Nash equilibrium concept or the strong Nash equilibrium concept. If a neutral social function is monotonic and simple, then the social function is fully implementable by a set of Nash equilibria. For finite alternative sets a neutral social function will be fully implementable by a set of strong Nash equilibria if and only if it is monotonic, simple and dictatorial.     

When Does a Platform Create Value by Limiting Choice?

We present a theory for why it might be rational for a platform to limit the number of applications available on it. Our model is based on the observation that even if users prefer application variety, applications often also exhibit direct network effects. When there are direct network effects, users prefer to consume the same applications to benefit from consumption complementarities. We show that the combination of preference for variety and consumption complementarities gives rise to (i) a commons problem (to better satisfy their individual preference for variety, users have an incentive to consume more applications than the number that maximizes joint utility); (ii) an equilibrium selection problem (consumption complementarities often lead to multiple equilibria, which result in different utility levels for the users); and (iii) a coordination problem (lacking perfect foresight, it is unlikely that users will end up buying the same set of applications). The analysis shows that the platform can resolve these problems and create value by limiting the number of applications available. By limiting choice, the platform may create new equilibria (including the allocation that maximizes users' utility); eliminate equilibria that give lower utility to the users; and reduce the severity of the coordination problem faced by users.     

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.