The Old‐Boy Network and the Quality of Entrepreneurs

We study a model of network formation and start‐up financing with endogenous entrepreneurial type distribution. A hub firm admits members to its network based on signals about entrepreneurs' types. Network membership is observable, which allows lenders to offer different interest rates to network and stand‐alone entrepreneurs. We show that a network outcome can display a smaller number of high‐type entrepreneurs even though the network is neither nepotistic nor informationally disadvantaged. Although a welfare‐improving network can emerge as a technically stable or unstable equilibrium, one that decreases welfare is always formed by a technically unstable equilibrium. However, the adverse welfare effects of a network and its corresponding type configuration may persist because ex post high‐type entrepreneurs prefer to stay high type whereas those who wish to become high type may need some time to react.     

Incentivizing resilience in financial networks

When banks extend loans to each other, they generate a negative externality in the form of systemic risk. They create a network of interbank exposures by which they expose other banks to potential insolvency cascades. In this paper, we show how a regulator can use information about the financial network to devise a transaction-specific tax based on a network centrality measure that captures systemic importance. Since different transactions have different impact on creating systemic risk, they are taxed differently. We call this tax a systemic risk tax (SRT). We use an equilibrium concept inspired by the matching markets literature to show analytically that this SRT induces a unique equilibrium matching of lenders and borrowers that is systemic-risk efficient, i.e. it minimizes systemic risk given a certain transaction volume. On the other hand, we show that without this SRT multiple equilibrium matchings exist, which are generally inefficient. This allows the regulator to effectively stimulate a ‘rewiring’ of the equilibrium interbank network so as to make it more resilient to insolvency cascades, without sacrificing transaction volume. Moreover, we show that a standard financial transaction tax (e.g. a Tobin-like tax) has no impact on reshaping the equilibrium financial network because it taxes all transactions indiscriminately. A Tobin-like tax is indeed shown to have a limited effect on reducing systemic risk while it decreases transaction volume.     

Competitive General Equilibrium with network externalities

We identify sufficient conditions for existence of competitive equilibrium with network externalities and indivisibilities. Such combination of externalities and indivisibilities is present in many goods and services with network effects, and it makes existence of equilibrium non-trivial. We provide an existence theorem in a model with a measure space of consumers. Key conditions for existence are anonymity of network effects and dispersion in the economy’s income distribution.     

A Strategic Approach to Software Protection*

This paper demonstrates that there is a strategic reason why software firms have followed consumers' desire to drop software protection. We analyze software protection policies in a price-setting duopoly software industry selling differentiated software packages, where consumers' preference for particular software is affected by the number of other consumers who (legally or illegally) use the same software. Increasing network effects make software more attractive to consumers, thereby enabling firms to raise prices. However, it also generates a competitive effect resulting from feircer competition for market shares. We show that when network effects are strong, unprotecting is an equilibrium for a noncooperative industry.     

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.     

Incorporating Transportation Network Structure in Spatial Econometric Models of Commodity Flows

Abstract

We use a spatial econometric extension of the traditional regression-based gravity model to model commodity flows, focusing on a formal methodology for incorporating information regarding the highway network into the spatial connectivity structure of the spatial autoregressive econometric model. We show that our simple approach to incorporating this information in the model produces improved model fit and higher likelihood function values. Empirical estimates of the relative importance of the different types of origin–destination connectivity between regions indicates that the strongest spatial autoregressive effects arise when both origin and destination regions have neighbouring regions located on the highway network.     

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.     

Isomorphic multiclass spatial price and multimodal traffic network equilibrium models

In this paper, we first show that a multiclass spatial price equilibrium model can be formulated as an equivalent multimodal traffic network equilibrium model with special structure. This connection allows us to obtain, for the multiclass spatial price equilibrium model, in a routine manner, any information that is currently available in the well developed theory of the general multimodal network equilibrium model, and moreover, to strengthen a number of these results taking advantage of the special structure of the equivalent multimodal traffic network model.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

Apple's disaster: Linking two‐sided markets and strategic delegation

Asymmetric pricing structure and different intergroup network externalities are characteristics of two‐sided markets not captured in the analysis of one‐sided markets. Focusing on Cournot duopoly where membership decision may be delegated to a manager, several equilibrium regimes are sustained depending on the fixed cost of managerial hiring and strength of the network externality exerted by the side whose demand is more price sensitive. The change from null to full delegation sharpens the asymmetric pricing structure and reduces the price level in two‐sided markets. Contrary to one‐sided markets with direct network effects, the prisoner's dilemma holds for sufficiently strong indirect network externalities. Imperfect interside discrimination of managerial incentives ensures profit maximization and efficient consumers' allocation. Private hiring should occur when the two‐sided market exhibits symmetric pricing structure. An explanation for Apple's unprecedented event is provided. The reduction of revenue and managerial bonus in 2016 may be justified by the dissemination of full delegation in the Chinese information technology industry. Apple's upcoming strategy may consist on reducing both access prices, although the side whose demand is more price sensitive should have a greater price reduction. Alternatively, improving the content quality may constitute Apple's corporate strategy, thereby inducing a skimming pricing strategy on Chinese rivals.     

Learning and coordination with dispersed information

We analyse adaptive learning in a model of incomplete and dispersed information, with externalities and strategic interactions. We build on the framework proposed by Angeletos and Pavan (2007a) and extend it to a dynamic multi-period setting where agents need to learn to coordinate. We derive conditions under which adaptive learning obtains in such setting and show that, when actions are strategic substitutes, the information structure affects the speed of convergence: while more precise private information is beneficial, better public information has negative effects. We also show that adaptive learning dynamics converge to the Bayesian Nash equilibrium, which means that agents can learn to act strategically by relying only on observable (exogenous) information.     

The impact of lead time on capital investments

We study equilibrium investment strategies of firms competing in stochastic dynamic market settings and facing two types of investment structures: investment with significant lead time (or time-to-build) and investment without (or minor) lead time. We investigate how investment behavior changes when investment is subject to time-to-build versus when it is not. We characterize equilibrium investment strategies under several information structures and compare results to the social optimum. We offer some new results. The model predicts that, controlling for demand, and production and investment costs, investments and outputs can be higher in progressive industries (which often exhibit time-to-build) than in fast-paced industries (where time-to-build is insignificant). Furthermore, for both investment types (investment with or without time-to-build) we offer a novel equilibrium in which firms incrementally invest. This behavior is driven by demand uncertainty and capacity constraints. Also, expected outputs are lower than Cournot outputs as firms face uncertainty. Moreover, the amount of uncertainty has different effects over investment types.     

Quality of Information and Oligopolistic Price Discrimination

Recent developments in information technology (IT) have resulted in the collection of a vast amount of customer-specific data. As IT advances, the quality of such information improves. We analyze a unifying spatial price discrimination model that encompasses the two most studied paradigms of two-group and perfect discrimination as special cases. Firms use the available information to classify the consumers into different groups. The number of identifiable consumer segments increases with the information quality. Among our findings (1) when the information quality is low, unilateral commitments not to price discriminate arise in equilibrium; (2) after a unique threshold of information precision such a commitment is a dominated strategy, and the game becomes a prisoners' dilemma; and (3) equilibrium profits exhibit a U-shaped relationship with the information quality.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

An equilibrium model of insider trading in continuous time

We study a Bayesian–Nash equilibrium model of insider trading in continuous time. The supply of the risky asset is assumed to be stochastic. This supply can be interpreted as noise from nonrational traders (noise traders). A rational informed investor (the insider) has private information on the growth rate of the dividend flow rewarded by the risky asset. She is risk averse and maximizes her inter-temporal utility rate over an infinite time-horizon. The market is cleared by a risk neutral market maker who sets the price of the risky asset competitively as the conditional present value of future dividends, given the information supplied by the dividend history and the cumulative order flow. Due to the presence of noise traders, the market demand does not fully reveal the insider’s private information, which slowly becomes incorporated in prices. An interesting result of the paper is that a nonstandard linear filtering procedure gives an a priori form for the equilibrium strategy to be postulated. We show the existence of a stationary linear equilibrium where the insider acts strategically by taking advantage of the camouflage provided by the noise which affects the market maker’s estimates on private information. In this equilibrium, we find that the insider’s returns on the stock are uncorrelated over long periods of time. Finally, we show that the instantaneous variance of the price under asymmetric information lies between the instantaneous variance of the price under complete and incomplete information. The converse inequalities hold true for the unconditional variance of the price.     

Coordinating under incomplete information

We show that, in a minimum effort game with incomplete information where player types are independently drawn, there is a largest and smallest Bayesian equilibrium, leading to the set of equilibrium payoffs (as evaluated at the interim stage) having a lattice structure. Furthermore, the range of equilibrium payoffs converges to those of the deterministic complete information version of the game, in the limit as the incomplete information vanishes. This entails that such incomplete information alone cannot explain the equilibrium selection suggested by experimental evidence. We thank Atila Abdulkadiroglu, Hans Carlsson, Ani Guerdjikova and an anonymous referee for helpful comments. Part of this work was done while Asheim was visiting Cornell University, which hospitality is gratefully acknowledged.     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

基于Multi-Agent技术的交通网络均衡模型

基于Multi-Agent技术,建立了一个交通网络均衡模拟模型。通过Agent的思想来描述网络中不同个体的行为决策,及其共同作用对整个网络产生的影响。模型结合经典均衡理论,为复杂的均衡点求解问题提供了直观、简洁的求解方式。     

Product Differentiation and Upstream-Downstream Relations

This paper examines the relationship between a differentiated downstream market and a specialized upstream market. We analyze three different types of vertical relation between the upstream and downstream sectors when the upstream market supplies specialized and complementary inputs to a downstream product-differentiated market. The first is the benchmark case of decentralized markets, the second is a network of alliances among upstream suppliers, and the third is partial vertical integration. We identify the perfect equilibrium for a symmetric model in each case and show that there is no simple relationship between the degree of connection between upstream and downstream firms and profitability. The key factor affecting prices and the relative profitability of the different market organizations is the degree of product differentiation among the downstream firms, because it affects the intensity of competition among upstream suppliers. We show that vertical foreclosure is not an equilibrium strategy.