Price discrimination via information provision

We study price discrimination where different prices are offered as a bundle with different levels of information about a product. The seller’s price discrimination induces high valuation buyers to purchase a good without information and low valuation buyers to purchase with information. Our analysis highlights several interesting results about price discrimination: (i) the seller’s choice of information provision is the combination of full information and no information, (ii) products can be cheaper without information provision than with information provision, (iii) as a result of price discrimination, prices can be more dispersed as buyers’ valuations become largely similar, and (iv) the high valuation buyers purchase a damaged good and may earn negative surplus. Furthermore, we investigate under which circumstances price discrimination is more profitable than uniform pricing. We show that a decline in transportation costs which facilitate price discrimination can be welfare reducing.     

Nonstandard foundations of equilibrium search models

We develop an equilibrium sequential search model which includes most of the literature as special cases. In particular, the model can accommodate heterogeneity in buyers’ search costs and demand functions and firms’ cost functions, with general demand and cost functions. We identify conditions which ensure existence of equilibrium in pure strategies, utilizing recent progress in the theory of large games by Khan and Sun. These conditions elucidate the essential structure of equilibrium search models. Although we focus on sequential search, our methodology can be used for other classes of equilibrium search models as well.     

Free and second-best entry in oligopolies with network effects

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business-stealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.     

Reserve price signaling

In a general auction model in which bidders’ signals are affiliated, we characterize the unique separating equilibrium in which the seller can use reserve prices to credibly signal her private information. When the buyers’ signals are independent, the optimal reserve price is shown to be increasing in the number of bidders under certain conditions. We also demonstrate that the probability that the item is sold at the reserve price can increase as the number of bidders increases, which indicates a more central role for reserve prices than perceived in the standard auction models.     

A theory of commerce

The theory of commerce advanced here captures prominent features of retail trade: large employment, congestion effects, anonymous posted prices, and quantity discounts. This theory is built around a directed search model where buyers’ preferences are private information. The analytical solution is easily inserted in a Neoclassical growth framework. In this framework, the parameters of retail trade are calibrated using commercial margins and employment. Welfare properties depend on the sellers’ ability to charge two-tier prices. With two-tier prices, the directed search equilibrium is efficient. Otherwise, it is not. This contrasts with the full information benchmark, where directed search is always efficient.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Search and endogenous concentration of liquidity in asset markets

We develop a search-based model of asset trading, in which investors of different horizons can invest in two assets with identical payoffs. The asset markets are partially segmented: buyers can search for only one asset, but can decide which one. We show the existence of a “clientele’’ equilibrium where all short-horizon investors search for the same asset. This asset has more buyers and sellers, lower search times, and trades at a higher price relative to its identical-payoff counterpart. The clientele equilibrium dominates the one where all investor types split equally across assets, implying that the concentration of liquidity is socially desirable.     

Mechanism Design with Interdependent Valuations: Surplus Extraction

If valuations are interdependent and agents observe their own allocation payoffs, then two-stage revelation mechanisms expand the set of implementable decision functions. In a two-stage revelation mechanism agents report twice. In the first stage - before the allocation is decided - they report their private signals. In the second stage - after the allocation has been made, but before final transfers are decided - they report their payoffs from the allocation. Conditions are provided under which an uninformed seller can extract (or virtually extract) the full surplus from a sale to privately informed buyers, in spite of the buyers’ signals being independent random variables. This research was started when I was visiting the Department of Applied Mathematics of the University of Venice, and continued while visiting the European University Institute in Florence. Their financial support is gratefully acknowledged.     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

Financial opening, deposit insurance, and risk in a model of banking competition

We study the impact of competition on banks’ risk-taking behavior under different assumptions about deposit insurance and the dissemination of information. While financial opening increases banks’ riskiness, a risk-based deposit insurance or, alternatively, the public disclosure of financial information, are likely to mitigate this effect. Moreover, the limiting cases of uninsured but fully informed depositors, and risk-based full deposit insurance, yield the same equilibrium risk level. Although the welfare consequences of increased competition depend on its impact on risk, financial opening unambiguously improves welfare as we approach the limiting cases.     

PROFITABLE STRATEGIC DELEGATION WITH CONJECTURAL VARIATIONS

Firms delegate strategic decisions to managers because they find it profitable to do so. In the product market, when agents make conjectures about the reaction of their rivals to marginal changes in their own strategies, the set of equilibriums can be enlarged with respect to the case of no conjectures. This paper takes a duopolistic linear market parameterization where firms selling differentiated products can delegate either price or output decisions to managers. We show that it is a dominant strategy for firms to delegate no matter whether firms are Cournot or Bertrand competitors, although the equilibrium is not necessarily efficient. Futhermore, in equilibrium Cournot competition is more profitable for firms than Bertrand competition. Finally, requiring consistency in conjectures yields the same outcome no matter what type of strategic interaction and managerial choice there is on the part of firms.     

The Shill Bidding Effect versus the Linkage Principle

The analysis of second price auctions with externalities is utterly modified if the seller is unable to commit not to participate in the mechanism. For the General Symmetric Model introduced by Milgrom and Weber [P. Milgrom, R. Weber, A theory of auctions and competitive bidding, Econometrica 50 (1982) 1089-1122] we characterize the full set of separating equilibria that are symmetric among buyers and with a strategic seller being able to bid in the same way as any buyer through a so-called shill bidding activity. The revenue ranking between first and second price auctions is different from the one arising in Milgrom and Weber: the benefits from the highlighted ‘Linkage Principle’ are counterbalanced by the ‘Shill Bidding Effect.’     

INTERTEMPORAL COURNOT AND WALRAS EQUILIBRIA: AN ILLUSTRATION*

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an inefficiency that does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., it moves towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., it moves away from the Walrasian amount). "S'il y avait 3, 4, ...n producteurs en concurrence [...] la valeur de p, qui en résulte, diminuerait indéfiniment par l'accroissement indéfini du nombre n,”A. A. Cournot (1838, p. 63)."     

Costly risk verification without commitment in competitive insurance markets

This paper analyzes the equilibrium of an insurance market where applicants for insurance have a duty of good faith when they reveal private information about their risk type. Insurers can, at some cost, verify the type of insureds who file a claim and they are allowed to retroactively void the insurance contract if it is established that the policyholder has misrepresented his risk when the contract was taken out. However, insurers cannot precommit to their risk verification strategy. The paper analyzes the relationship between second-best Pareto-optimality and the insurance market equilibrium in a game theoretic framework. It characterizes the contracts offered at equilibrium, the individuals' contract choice as well as the conditions under which an equilibrium exists.     

To be consumed with moderation

We study the optimal behavior of a hyperbolic discounting agent who has incomplete information about his own preferences and can only learn them through consumption. We show that, even if moderate current consumption and moderate future consumption always dominates abstinence, the agent may optimally decide not to consume as a commitment device against inefficient learning that would lead to future excesses. This provides a rationale for why smokers, gamblers or compulsive buyers stick to second-best personal rules of behavior - such as “abstinence” - without invoking standard habit formation arguments. We also study how urges modify the strategy of the individual.     

Strongly robust equilibrium and competing-mechanism games

This paper formulates the notion of a strongly robust equilibrium relative to a set of mechanisms specified in any competing-mechanism game of complete information with multiple principals and multiple agents. It shows that when agents’ efforts are contractible, any strongly robust pure-strategy equilibrium relative to single-incentive contracts persists, regardless of the continuation equilibrium that agents play upon any principal's deviation to any complex mechanism.     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

On the welfare implications of restricting bankruptcy information

The Fair Credit Reporting Act (FCRA) dictates that adverse events such as a Chapter 7 bankruptcy filing must be removed from an individual’s credit record after 10 years. The intent of the law is to provide partial consumption insurance by giving an individual a fresh start. However, the law obviously weakens incentives not to default, which can result in higher interest rates that in turn reduce intertemporal insurance. Because of this tradeoff, it is unclear how long is the optimal length of time that an adverse event remains on an individual’s credit record. In this paper we assess the welfare consequences of varying the length of time that adverse events can be on one’s credit record. We calibrate the model to US data where the exclusion parameter is set to be 10 years on average. Then we run a counterfactual to find the length that maximizes ex-post economywide welfare using a consumption equivalent measure. The model predicts agents prefer to remove the bankruptcy flag after one year, though the gains are small.     

农民工职业风险、工伤保险与教育补贴的政策效应

农民工工伤保险和农民工教育补贴新政策引人瞩目。文章考虑两部门(农民工和政府)、两时期(教育投资期和工作期)经济,构造基于职业风险、并纳入新政策变量的效用函数,通过局部均衡和比较静态分析揭示新政策效应。结论表明:“理性选择”是农民工微观行为决策的特征雏型;农民工工伤保险制度实现了高、低风险职业福利的再分配;教育投资提升了社会效率,但均衡是帕累托次优状态;而农民工教育补贴政策的介入,则实现着帕累托改进的动态过程。农民工工伤保险和教育补贴政策的有机搭配,诠释着公平与效率并重的和谐政策艺术,动态支撑着公平与效率的平衡。     

Insurance market games: Scale effects and public policy

We propose a game-theoretic model to study various effects of scale in an insurance market. After reviewing a simple static model of insurer solvency (in which all customers have inelastic demand), we present a one-period game in which both the buyers and sellers of insurance make strategic bids to determine market price and quantity. For the case in which both buyers and sellers are characterized by constant absolute risk aversion, we show that a unique market equilibrium exists under certain conditions. For the special case of risk-neutral insurers, we then consider how both the price and quantity of insurance, as well as other quantities of interest to public-policy decision makers, are affected by the number of insurance firms, the number of customers, and the total amount of capital provided by investors.