Rationing in IPOs

We provide a model of bookbuilding in IPOs, in which the issuer can choose to ration shares. We consider two allocation rules. Under share dispersion, before informed investors submit their bids, they know that, in the aggregate, winning bidders will receive only a fraction of their demand. We demonstrate that this mitigates the winner’s curse, that is, the incentive of bidders to shade their bids. It leads to more aggressive bidding, to the extent that rationing can be revenue-enhancing. In a parametric example, we characterize bid and revenue functions, and the optimal degree of rationing. We show that, when investors’ information is diffuse, maximal rationing is optimal. Conversely, when their information is concentrated, the seller should not ration shares. We determine the optimal degree of rationing in a class of credible mechanisms. Our model reconciles the documented anomaly that higher bidders in IPOs do not necessarily receive higher allocations.IPOs

Making Money: Commercial Banks, Liquidity Transformation and the Payment System

We consider the interaction between the roles of a bank as a facilitator of payments in the economy and as a lender. In our model, banks make loans by issuing digital claims to an entrepreneur, who then uses them to pay for inputs. Issuing digital claims has two effects on a bank’s liquidity. First, some of these claims used as payment are cashed in before the project is over, necessitating transfers in the inter-bank market to meet these intermediate liquidity needs. Second, the lending bank must transfer reserves to the other banks when the project is done to settle its claims. Each of these transfers has a cost; the endogenous interest rate in the inter-bank market and a settlement cost for final transfers. These costs, in turn, are frictions that affect bank lending. Banks in our model are strategic. If productivity is similar, a high cost of final transfers leads to a coordination friction and multiple equilibria, with each bank trying to match the average number of digital claims issued by other banks. We consider the effects of financial innovations (i.e., FinTech) on the payments system and show that a reduction in the need for intermediate liquidity can lead to an increase in the inter-bank interest rate, because it also induces each bank to increase its lending. We also show that innovations may shift investments from more productive to less productive regions.http://deepblue.lib.umich.edu/bitstream/2027.42/136094/1/1337_Rajan.pd

Equilibria in a Hotelling Model: First-Mover Advantage?

We study a generalized Hotelling duopoly in which a consumer's net utility from a product depends on the location of product and consumer in product attribute space, a random utility term that captures idiosyncratic preferences, and the price of the product. Our model allows us to vary the relative impact of product attribute preferences (i.e., location) and idiosyncratic preferences on consumer utility. Since the model is analytically intractable, we computationally study equilibria under both simultaneous location and sequential location by the two .rms, with prices decided simultaneously after locations have been chosen. In our numerical analysis, the simultaneous game admits only symmetric equilibria. If product attribute preferences are weak (i.e., distance costs are unimportant) and idiosyncratic preferences are also weak, both .rms locate in the interior of the feasible location space. With strong product attribute preferences and weak idiosyncratic preferences, price competition is at its most intense, leading to maximal di.erentiation. As idiosyncratic preferences become more important, price competition is mitigated, leading to both .rms locating at the market center. In the sequential game, we .nd that when product attribute preferences are strong and idiosyncratic preferences are weak, the follower has a strong desire to avoid price competition and the leader experiences a .rst-mover advantage. However, if idiosyncratic preferences are also strong, price competition is somewhat weaker, and the leader cedes a location and pro.t advantage to the follower. If product attribute preferences and idiosyncratic preferences are both weak, maximal di.erentiation results, and entry order is irrelevant. Finally, when idiosyncratic preferences dominate, price competition is a non-issue, and both players locate at the market center. Once again, the order of entry does not matter.http://deepblue.lib.umich.edu/bitstream/2027.42/60961/1/1114_Rajan.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/60961/4/1114_12_08_Rajan.pd

Robust Security Design

We consider the optimal contract between an entrepreneur and investors in a single-period model when both parties have limited liability, are risk-neutral toward cash flow risk, and are ambiguity-averse. Ambiguity aversion is modeled by multiplier preferences for robustness toward model uncertainty, as in Hansen and Sargent (2001). Efficient ambiguity-sharing implies that the first-best contract consists of either convertible debt or levered equity. As is customary, in the second-best contract, moral hazard is alleviated by giving more cash to investors in low cash flow states. Under many settings in our model, the optimal security has an equity-like component in high cash flow states, providing a contrast to the results in Innes (1990).http://deepblue.lib.umich.edu/bitstream/2027.42/136095/1/1338_Lee.pd

Personalized Pricing and Quality Differentiation on the Internet

No changes were made in the Abstract. Please use the previous Abstract that was submittedVertical Differentiation, Personalization, Price Discrimination, Electronic Commerce,

On multiple agent models of moral hazard

In multiple principal, multiple agent models of moral hazard, we provide conditions under which the outcomes of equilibria in direct mechanisms are preserved when principals can offer indirect communication schemes. We discuss the role of random allocations and recommendations and relate the result to the existing literature.Moral Hazard, Multiple Agents, Direct Mechanism.

Strategic Impact of Internet Referral Services on Channel Profits

Internet Referral Services, hosted either by independent third-party infomediaries or by manufacturers serve as âÃÂÃÂlead-generatorsâÃÂàin electronic marketplaces, directing consumer traffic to particular retailers. In a model of price dispersion with mixed strategy equilibria, we investigate the competitive implications of these institutions on retailer and manufacturer pricing strategies as well as their impact on channel structures and distribution of profits. Offline, retailers face a higher customer acquisition cost. In return, they can engage in price discrimination. Online, they save on the acquisition costs, but lose the ability to price discriminate. This critical tradeoff drives firmsâÃÂàequilibrium strategies. The establishment of a referral service is a strategic decision by the manufacturer, in response to a third-party infomediary. It leads to an increase in channel profits and a reallocation of the increased surplus to the manufacturer, via the franchise fees. Further, it enables the manufacturer to respond to an infomediary, by giving itself a wider leeway to set the unit wholesale fee to the profit maximizing level. We discuss implications of referral services on channel coordination issues, and whether a two part tariff can be successfully used to maximize channel profits. Contrary to prior literature, we find that when retailers can price discriminate among consumers, the manufacturer may not set the wholesale price to marginal cost to coordinate the channel. Consistent with anecdotal evidence, our model predicts that while it is optimal for an infomediary to enroll only one retailer, it is optimal for a manufacturer to enroll both retailers. Finally, our results show that under some circumstances, the manufacturer even benefits from the presence of the competing referral infomediary and hence, will not want to eliminate it.Information Systems Working Papers Serie

The Impact of Internet Referral Services on a Supply Chain

In many industries, Internet referral services, hosted either by independent third-party infomediaries or by manufacturers, serve as digitally enabled lead generators in electronic markets, directing consumer traffic to downstream retailers in a distribution network. This reshapes the extended enterprise from the traditional network of upstream manufacturers and downstream retailers to include midstream third-party and manufacturerowned referral services in the supply chain. We model competition between retailers in a supply chain with such digitally enabled institutions and consider their impact on the optimal contracts among the manufacturer, referral intermediary, and the retailers. Offline, retailers face a higher customer discovery cost. In return, they can engage in price discrimination based on consumer valuations. Online, they save on the discovery costs but lose the ability to identify consumer valuations. This critical trade-off drives firms’ equilibrium strategies. We derive the optimal contracts for different entities in the supply chain and highlight how these contracts change with the entry of independent and manufacturer-owned referral services. The establishment of a referral service is a strategic decision by the manufacturer. It leads to diversion of supply chain profit from a third-party infomediary to the manufacturer. Further, it enables the manufacturer to respond to an infomediary, by giving itself greater flexibility in setting the unit wholesale fee to the profit-maximizing level. Both third-party and manufacturer-sponsored referral services play a critical role in enabling retailers to discriminate across consumers’ different valuations. Retailers use online referral services to screen out low-valuation consumers and sell only to high-valuation consumers in the online channel. Our model thus endogenously derives a correlation between consumer valuation and online purchase behavior. Finally, we show that under some circumstances, it is too costly for the manufacturer to eliminate the referral infomediaryNYU, Stern School of Business, IOMS Department, Center for Digital Economy Researc

Personalized Pricing and Quality Differentiation

We develop an analytical framework to investigate the competitive implications of personalized pricing (PP), whereby firms charge different prices to different consumers, based on their willingness to pay. We embed personalized pricing in a model of vertical product differentiation, and show how it affects firmsâÃÂàchoices over quality. We show that firmsâÃÂàoptimal pricing strategies with PP may be non-monotonic in consumer valuations. When the PP firm has a high quality both firms raise their qualities, relative to the uniform pricing case. Conversely, when the PP firm has low quality, both firms lower their qualities. Although many firms are trying to implement such pricing policies, we find that a higher quality firm can actually be worse off with PP. While it is optimal for the firm adopting PP to increase product differentiation, the non-PP firm seeks to reduce differentiation by moving in closer in the quality space. While PP results in a wider market coverage, it also leads to aggravated price competition between firms. Since this entails a change in equilibrium qualities, the nature of the cost function determines whether firms gain or lose by implementing such PP policies. Despite the threat of first-degree price discrimination, we find that personalized pricing with competing firms can lead to an overall increase in consumer welfare.Information Systems Working Papers Serie