Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

Managing Risks in Multiple Online Auctions: An Options Approach*

The scenario of established business sellers utilizing online auction markets to reach consumers and sell new products is becoming increasingly common. We propose a class of risk management tools, loosely based on the concept of financial options that can be employed by such sellers. While conceptually similar to options in financial markets, we empirically demonstrate that option instruments within auction markets cannot be developed employing similar methodologies, because the fundamental tenets of extant option pricing models do not hold within online auction markets. We provide a framework to analyze the value proposition of options to potential sellers, option‐holder behavior implications on auction processes, and seller strategies to write and price options that maximize potential revenues. We then develop an approach that enables a seller to assess the demand for options under different option price and volume scenarios. We compare option prices derived from our approach with those derived from the Black‐Scholes model ( Black & Scholes, 1973 ) and discuss the implications of the price differences. Experiments based on actual auction data suggest that options can provide significant benefits under a variety of option‐holder behavioral patterns.     

PRICE DISPERSION WITH DIRECTED SEARCH

We present a model that generates empirically plausible price distributions in directed search equilibrium. There are many identical buyers and many identical capacity‐constrained sellers who post prices. These prices can be renegotiated to some degree and the outcome depends on the number of buyers who want to purchase the good. In equilibrium all sellers post the same price, demand is randomly distributed, and there is sale price dispersion. Prices and distributions depend on market tightness and on the properties of renegotiation outcomes. In a labor market context, the model generates a strong empirical prediction. If workers can renegotiate the posted wage, then the model predicts a positively skewed and realistic‐looking density function of realized wages when the mean number of job‐seekers per vacancy is large. (JEL: C780, D390, D490, E390)     

Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?

We construct a quantitative equilibrium model with firms setting prices in a staggered fashion and use it to ask whether monetary shocks can generate business cycle fluctuations. These fluctuations include persistent movements in output along with the other defining features of business cycles, like volatile investment and smooth consumption. We assume that prices are exogenously sticky for a short time. Persistent output fluctuations require endogenous price stickiness in the sense that firms choose not to change prices much when they can do so. We find that for a wide range of parameter values, the amount of endogenous stickiness is small. Thus, we find that in a standard quantitative model, staggered price‐setting, alone, does not generate business cycle fluctuations.     

Limited Rationality and Strategic Interaction: The Impact of the Strategic Environment on Nominal Inertia

Much evidence suggests that people are heterogeneous with regard to their abilities to make rational, forward‐looking decisions. This raises the question as to when the rational types are decisive for aggregate outcomes and when the boundedly rational types shape aggregate results. We examine this question in the context of a long‐standing and important economic problem: the adjustment of nominal prices after an anticipated monetary shock. Our experiments suggest that two types of bounded rationality—money illusion and anchoring—are important behavioral forces behind nominal inertia. However, depending on the strategic environment, bounded rationality has vastly different effects on aggregate price adjustment. If agents' actions are strategic substitutes, adjustment to the new equilibrium is extremely quick, whereas under strategic complementarity, adjustment is both very slow and associated with relatively large real effects. This adjustment difference is driven by price expectations, which are very flexible and forward‐looking under substitutability but adaptive and sticky under complementarity. Moreover, subjects' expectations are also considerably more rational under substitutability.     

我国通货膨胀动态和货币政策效果的行为宏观解释

对中国1990～2005年季度数据的SVAR分析显示,货币政策的通胀效果是滞后的,而且通货膨胀表现出惯性的特征。本文通过对当前两类主流宏观模型的模拟发现:完全前瞻的新凯恩斯主义粘性价格模型不符合货币冲击的历史效果,而Mankiw等提出的粘性信息模型则具有更强的合理性。这一理论解释力方面存在的差别主要源自,新凯恩斯主义粘性信息模型保持着理性预期假设,而粘性信息模型对理性预期完全信息进行了放松。因此,粘性信息模型行为宏观经济模型为我国货币政策效果讨论和最优货币政策研究提供了更好的理论基础。     

The Dark Side of Information and Market Efficiency in E‐Markets*

Price dispersion reflects the differences in prices for identical products. While in physical markets such dispersion is prevalent due to high search costs, many researchers argue that search costs and price dispersion will be much lower in electronic markets (e‐markets). Empirical evidence does not support this contention, and researchers have studied search costs, market factors, and service‐quality factors to explain this dispersion. Previous research has largely assumed that more information is better. By ignoring the dark side of information, we argue that only a partial understanding of price dispersion is possible. In this article, information overload and equivocality are studied as two dark attributes of information that lead sellers to different pricing decisions in e‐markets. Hypotheses relating these attributes to price dispersion are supported through analysis of 161 product markets. This work opens up new avenues in the study of e‐markets and discusses the implications of these findings for research and practice on consumer and seller decisions.     

FAIR PRICING

This paper explores the consequences of supposing that consumers see a firm as fair if they cannot reject the hypothesis that the firm is somewhat benevolent towards them. When consumers can reject this hypothesis, some become angry, which is costly to the firm. The desire to appear benevolent can lead firms to adopt third‐degree price discrimination based on the income of different consumer classes while foreswearing third‐degree price discrimination based on differences in the elasticity of demand. It can also explain why prices seem to be more responsive to changes in factor costs than to changes in demand that have the same effect on marginal cost. Lastly, if consumers experience regret or disappointment when faced by increased prices, the model can explain why prices can be more rigid in response to disasters that increase demand dramatically than they are when there is a less substantial increase in demand.     

Group Buying,Buyer Heterogeneity,and Sellers' Bargaining Power*

Group buying enables collective bargaining opportunity that individual buyers lack to negotiate prices with sellers. This potential negotiation capability has two opposing effects. On the one hand, the prospect of the group being able to negotiate price with its rival forces each seller to lower its price offer, as too high a price will induce the group to give its rival an opportunity to undercut its price via negotiation, likely taking away all the buyers. On the other hand, the potential negotiation opportunity may also discourage sellers from competing aggressively in their price offers, as the benefit of charging a low price could be offset by competitors in negotiation, thus yielding overall higher prices for the buyers. In this study, we find that compared to individual purchase, buyers benefit from collective bargaining opportunity by group buying only if sellers’ bargaining power relative to the buyer group is low and/or buyers’ preferences toward the sellers are sufficiently differentiated. Given buyers’ strategic choice of group purchase, sellers may be worse off with a further increase in bargaining power, and so may social welfare.     

MATERIALS PRICES AND PRODUCTIVITY

There is substantial within‐industry variation in the prices that plants pay for their material inputs. Using plant‐level data from the US Census Bureau, I explore the consequences and sources of this variation in materials prices. For a sample of industries with relatively homogeneous products, the standard deviation of plant‐level productivity would be 7% smaller if all plants faced the same materials prices. Moreover, plant‐level materials prices are persistent, spatially correlated, and positively associated with the probability of exit. The contribution of entry and exit to aggregate productivity growth is smaller for productivity measures that are purged of materials price variation. After documenting these patterns, I discuss three potential sources of materials price variation: geography, differences in suppliers' marginal costs, and within‐supplier markup differences. Together, these variables explain 15% of the variation of materials prices.     

A Brief Review and Assessment of the Leegin Decision: Who Wins and Who Loses When Manufacturers Are Free to Set Retail Prices?

For decades, it has been a per se violation of U.S. antitrust law for manufacturers or distributors to specify retail selling prices. In the spirit of atomistic, unrestrained competition, retailers were free to set prices without undue interference from upstream channel participants. Attempts by manufacturers or other channel participants to restrict retail price setting initiatives were viewed by regulators as an unwarranted and illegal interference with the market mechanism. Restrictions on price setting initiatives would, it was argued, lessen competition and ultimately raise prices above competitive levels to the detriment of consumers. Recently, under the leadership of newly appointed Chief Justice Roberts, a more “business friendly” Supreme Court has reversed this policy; vertical price fixing is no longer a per se violation of U.S. antitrust law. By a five‐to‐four margin, the Court held in Leegin Creative Leather Products that manufacturers could, under certain circumstances, establish binding retail selling prices. Henceforth, retail price setting restrictions will be subject to a rule of reason evaluation whereby price restrictions will be assessed on a case‐by‐case basis. Proponents of the now‐legal restrictions argue that this will ensure that merchandise sold through retail outlets will receive needed support, free riding will be reduced or eliminated, and new brand introduction will be facilitated. Critics argue that the Court's decision marks a return to the days of fair trading; marginal firms will be protected, so‐called “inframarginal consumers” will be forced to pay for services they do not want or need, and prices for many branded products will rise, all to the detriment of consumer welfare.     

P2P Marketplaces and Retailing in the Presence of Consumers' Valuation Uncertainty

Can peer‐to‐peer (P2P) marketplaces benefit traditional supply chains when consumers may experience valuation risk? P2P marketplaces can mitigate consumers' risk by allowing them to trade mismatched goods; yet, they also impose a threat to retailers and their suppliers as they compete over consumers. Further, do profit‐maximizing marketplaces always extract the entire consumer surplus from the online trades? Our two‐period model highlights the effects introduced by P2P marketplaces while accounting for the platform's pricing decisions. We prove that with low product unit cost, the P2P marketplace sets its transaction fee to the market clearing price, thereby extracting all of the seller surplus. In this range of product unit cost, the supply chain partners are worse off due to the emergence of a P2P marketplace. However, when the unit cost is high, the platform sets its transaction fee to be less than the market clearing price, intentionally leaving money on the table, as a mechanism to stimulate first period demand for new goods in expectation for some of them to be traded later, in the second period, via the marketplace. It is not until the surplus left with the sellers is sufficiently high that the supply chain partners manage to extract some of this surplus, ultimately making them better off due to a P2P marketplace. We further analyze the impact of a P2P marketplace on consumer surplus and social welfare. In addition, we consider model variants accounting for a frictionless platform and consumer strategic waiting.     

Dynamic Monetary Equilibrium in a Random Matching Economy

This article concerns an infinite horizon economy where trade must occur pairwise, using a double auction mechanism, and where fiat money overcomes lack of double coincidence of wants. Traders are anonymous and lack market power. Goods are divisible and perishable, and are consumed at every date. Preferences are defined by utility‐stream overtaking. Money is divisible and not subject to inventory constraints. The evolution of individual and economywide money holdings distributions is characterized. There is a welfare‐ordered continuum of single price equilibria, reflecting indeterminacy of the price level rather than of relative prices.     

EQUIVALENCE RESULTS FOR OPTIMAL PASS‐THROUGH,OPTIMAL INDEXING TO EXCHANGE RATES,AND OPTIMAL CHOICE OF CURRENCY FOR EXPORT PRICING

Firms sometimes write price lists or catalogs for their exports, so they set prices for a period of time and do not adjust prices during that interval in response to changes in their environment. The firm sets the price either in its own currency or the importer's currency. This paper draws a simple link between the choice of currency and the pricing decision of a firm that changes prices in response to all shocks. Specifically, if the latter firm's price has a lower variance in terms of its own currency than the importer's currency, then the firm with a price list will set the price in its own currency (and otherwise it will set price in the foreign currency). This relationship is established by consideration of the firm with a price list as a special case of a firm that indexes its export price to the exchange rate. (JEL: F4, F1)     

PRICING,PRODUCTION, AND PERSISTENCE

Though built with increasingly precise microfoundations, modern optimizing sticky price models have displayed a chronic inability to generate large and persistent real responses to monetary shocks, as recently stressed by Chari, Kehoe, and McGrattan (2000). We trace this lack of persistence to a standard view of the cyclical behavior of real marginal cost built into current sticky price macro models. Using a fully articulated general equilibrium model, we develop an alternative perspective on real marginal cost that leads to substantial persistence. Based on an important role for materials input, variable capacity utilization, and labor adjustment on the extensive margin, this alternative view also makes the sticky price model display volatility and comovement of factor inputs and factor prices more closely in line with conventional wisdom about business cycles and various empirical studies of the dynamic effects of monetary shocks. (JEL: E31 E32)     

Uncertainty Shocks in a Model of Effective Demand

Can increased uncertainty about the future cause a contraction in output and its components? An identified uncertainty shock in the data causes significant declines in output, consumption, investment, and hours worked. Standard general‐equilibrium models with flexible prices cannot reproduce this comovement. However, uncertainty shocks can easily generate comovement with countercyclical markups through sticky prices. Monetary policy plays a key role in offsetting the negative impact of uncertainty shocks during normal times. Higher uncertainty has even more negative effects if monetary policy can no longer perform its usual stabilizing function because of the zero lower bound. We calibrate our uncertainty shock process using fluctuations in implied stock market volatility, and show that the model with nominal price rigidity is consistent with empirical evidence from a structural vector autoregression. We argue that increased uncertainty about the future likely played a role in worsening the Great Recession. The economic mechanism we identify applies to a large set of shocks that change expectations of the future without changing current fundamentals.     

基于VAR模型的油价波动对我国经济影响分析

本文运用VAR模型,构建了原油价格与经济增长、物价水平、货币政策、失业率之间的动态关系系统,着重探讨油价波动对我国一些重要经济变量,特别是经济增长的影响规律。Granger因果关系分析表明,油价波动是引起经济增长率、物价水平、货币政策等经济指标变化的Granger原因。通过VAR(2)模型及脉冲响应分析,油价上升对我国经济的主要影响有:不会使国内生产总值减少,但会使经济增长速度变缓;通过对总需求的拉动及成本增加这样两条途径使物价水平上升;长期内会使失业率增加;增加了有效实施货币政策的难度。整体来看,尽管国际油价及我国的经济变量复杂多变,由国际油价、经济增长、物价水平、货币供应量、失业率这五个变量所构成的经济系统是稳定的,也就是说,通过市场经济的自动调节和政府的宏观经济调控,我国的经济能够平稳有序的发展。     

Toward a Strategic Foundation for Rational Expectations Equilibrium

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double‐auction equilibrium is almost efficient and almost fully aggregates the agents' information.     

基于信号博弈的卖方欺诈行为分析

本文主要基于信号博弈的卖方欺诈行为进行研究，假设拍卖中可能存在欺诈型和诚实型两种卖家，其中欺诈行为有概率发生在第二价格拍卖中：欺诈型卖方冒充竞拍者递交仅次于最高价的报价从而获得额外收益。两种卖家根据各自效用选择拍卖形式：第一价格或者第二价格。而竞买者将卖者的选择作为信号，更新对卖方类型的判断，然后制定报价策略。这是一个买卖方信号交叉影响的过程。考虑到拍卖过程中买方价值相关性，本文在建立模型中参考了关联价值原理。针对该模型进行分析，得出了不同情况下的买卖方策略，并且研究了买方报价、买方判断、卖方收益三者之间的关系。文中利用贝叶斯公式对双方的策略选择问题进行预测，与单纯的概率分布方法相比，更具实践价值。     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.