Optimal Pricing of Two Successive‐Generation Products with Trade‐in Options under Uncertainty

To entice consumers to purchase both current and next generation products, many manufacturers and retailers offer trade‐in programs that allow buyers of the first generation product to trade‐in the product and purchase the new generation product at a lower price. By considering the interactions between “forward‐looking” consumers and a firm when a trade‐in program is offered, we analyze a two‐period dynamic game to determine the optimal prices of two successive‐generation products in equilibrium, and examine the conditions under which trade‐in programs are beneficial to the firm. Our model incorporates market heterogeneity (valuation of the first generation product varies among the consumer population), product uncertainty (the incremental value of the new product is uncertain before its introduction), and consumers' forward‐looking behavior (consumers take future product valuation and prices into consideration when making purchasing decisions). With the trade‐in option, we show that consumers are willing to pay a price that is higher than their valuations of the current product. Furthermore, trade‐in programs are more beneficial to the firm when: (i) the durability of the current product is high; (ii) the market heterogeneity is low; or (iii) the uncertainty level (or the expected incremental value) of the new product is high. Finally, when the incremental value of the new product is more uncertain, consumers are more willing to purchase the current product because of the “option” value of the trade‐in programs and thus trade‐in programs can be more beneficial to the firm in this case.     

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.     

Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

Advance Selling in the Presence of Speculators and Forward‐Looking Consumers

This article examines the pricing policy of a monopolist seller who may sell in advance of consumption in a market that comprises of myopic consumers, forward‐looking consumers, and speculators. The latter group has no consumption value for the goods and is in the market with the sole objective of making a profit by reselling the purchased goods shortly after. Consumers, although homogeneous in terms of their valuations, are different with respect to their perspectives. We show that in an “upward” market where the expected valuation increases over time, the optimal pricing policy is an ex ante “static” one where the seller “prices into the future” and prices the myopic consumers out of the advance market. However, in a “downward” market where the expected valuation decreases over time, the seller adopts a dynamic pricing strategy except for the case when higher initial sales can trigger more demand subsequently and when the downward trend is not too high. In this case, the seller prefers an ex ante “static” pricing strategy and deliberately prices lower initially to sell to speculators. We identify the conditions under which the seller benefits from the existence of speculators in the market. Moreover, although the presence of entry costs is ineffective as an entry deterrence, we determine the conditions under which exit costs can rein in speculative purchase.     

Efficient Multi‐Attribute Multi‐Unit Auctions for B2B E‐Commerce Logistics

This study is the first proposing allocatively efficient multi‐attribute auctions for the procurement of multiple items. In the B2B e‐commerce logistics problem (ELP), the e‐commerce platform is the shipper generating a large number of online orders between product sellers and buyers, and third‐party logistics (3PL) providers are carriers that can deliver these online orders. This study focuses on the ELP with multiple attributes (ELP‐MA), which is generally the problem of matching the shipper's online orders and 3PL providers given that price and other attributes are jointly evaluated. We develop a one‐sided Vickrey–Clarke–Groves (O‐VCG) auction for the ELP‐MA. The O‐VCG auction leads to incentive compatibility (on the sell side), allocative efficiency, budget balance, and individual rationality. We next introduce the concept of universally unsatisfied set to construct a primal‐dual algorithm, also called the primal‐dual Vickrey (PDV) auction. We prove that the O‐VCG auction can be viewed as a single‐attribute multi‐unit forward Vickrey (SA‐MFV) auction. Both PDV and SA‐MFV auctions realize VCG payments and truthful bidding for general valuations. This result reveals the underlying link not only between single‐attribute and multi‐attribute auctions, but between static and dynamic auctions in a multi‐attribute setting.     

MARKET POWER AND INFORMATION REVELATION IN DYNAMIC TRADING

We study a strategic model of dynamic trading where agents are asymmetrically informed over common value sources of uncertainty. There is a continuum of buyers and a finite number n of sellers. All buyers are uninformed, while at least one seller is privately informed about the true state of the world. When n = 1, full information revelation never occurs in equilibrium and the only information transmission happens in the first period. With n > 1 the outcome depends both on the structure of the sellers' information and, even more importantly, on the intensity of competition allowed by the existing trading rules. When there is intense competition (absence of clienteles), information is fully and immediately revealed to the buyers in every equilibrium for n large enough, regardless of the number of informed sellers. On the other hand, for trading arrangements characterized by less intense forms of competition (presence of clienteles), for any n we always have equilibria where information is never fully revealed. Moreover, in that case, when only one seller is informed, for many parameter configurations there are no equilibria with full information revelation, even for large n. (JEL: C72, C78, D82, D83)     

Nonexclusive Competition in the Market for Lemons

A seller can trade an endowment of a perfectly divisible good, the quality of which she privately knows. Buyers compete by offering menus of nonexclusive contracts, so that the seller can privately trade with several buyers. In this setting, we show that an equilibrium exists under mild conditions and that aggregate equilibrium allocations are generically unique. Although the good for sale is divisible, in equilibrium the seller ends up trading her whole endowment or not trading at all. Trades take place at a price equal to the expected quality of the good, conditional on the seller being ready to trade at that price. Our model thus provides a novel strategic foundation for Akerlof's (1970) results. It also contrasts with competitive screening models in which contracts are assumed to be exclusive, as in Rothschild and Stiglitz (1976). Latent contracts that are issued but not traded in equilibrium play an important role in our analysis.     

Precautionary Bidding in Auctions

We analyze bidding behavior in auctions when risk‐averse buyers bid for a good whose value is risky. We show that when the risk in the valuations increases, DARA bidders will reduce their bids by more than the appropriate increase in the risk premium. Ceteris paribus, buyers will be better off bidding for a more risky object in first price, second price, and English auctions with affiliated common (interdependent) values. This “precautionary bidding” effect arises because the expected marginal utility of income increases with risk, so buyers are reluctant to bid so highly. We also show that precautionary bidding behavior can make DARA bidders prefer bidding in a common values setting to bidding in a private values one when risk‐neutral or CARA bidders would be indifferent. Thus the potential for a “winner's curse” can be a blessing for rational DARA bidders.     

Cursed Equilibrium

There is evidence that people do not fully take into account how other people's actions depend on these other people's information. This paper defines and applies a new equilibrium concept in games with private information, cursed equilibrium, which assumes that each player correctly predicts the distribution of other players' actions, but underestimates the degree to which these actions are correlated with other players' information. We apply the concept to common‐values auctions, where cursed equilibrium captures the widely observed phenomenon of the winner's curse, and to bilateral trade, where cursedness predicts trade in adverse‐selections settings for which conventional analysis predicts no trade. We also apply cursed equilibrium to voting and signalling models. We test a single‐parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values that correspond to cursedness fit a broad range of experimental datasets better than the parameter value that corresponds to Bayesian Nash equilibrium.     

Reputation for Quality

We propose a model of firm reputation in which a firm can invest or disinvest in product quality and the firm's reputation is defined as the market's belief about this quality. We analyze the relationship between a firm's reputation and its investment incentives, and derive implications for reputational dynamics. Reputational incentives depend on the specification of market learning. When consumers learn about quality through perfect good news signals, incentives decrease in reputation and there is a unique work–shirk equilibrium with ergodic dynamics. When learning is through perfect bad news signals, incentives increase in reputation and there is a continuum of shirk–work equilibria with path‐dependent dynamics. For a class of imperfect Poisson learning processes and low investment costs, we show that there exists a work–shirk equilibrium with ergodic dynamics. For a subclass of these learning processes, any equilibrium must feature working at all low and intermediate levels of reputation and shirking at the top.     

TRADE QUOTAS AND BUYER POWER,WITH AN APPLICATION TO THE E.U. NATURAL GAS MARKET

We consider a market in which domestic buyers negotiate contracts with foreign sellers, and explore how trade quotas can help to increase the buyers' countervailing power. We use the Shapley value to describe bargaining power and the distribution of the trade surplus in such a bilateral oligopoly. By exploiting strategic externalities among the buyers, bilateral trade quotas can improve the buyers' bargaining positions. In contrast, aggregate trade restrictions on all buyers' trade never improve buyer surplus. Minimum quotas on imports from fringe suppliers can benefit nonaffected buyers, as these enjoy positive externalities. We apply these insights to the E.U. market for natural gas and show that the effects of trade quotas on E.U. gas importers' power can be significant.     

Competition and Coordination in Online Marketplaces

Online marketplaces, such as those operated by Amazon, have seen rapid growth in recent years. These marketplaces serve as an intermediary, matching buyers with sellers, whereas control of the good is left to the seller. In some cases, e.g., the Amazon marketplace system, the firm that owns and manages the marketplace system will also sell competing products through the marketplace system. This creates a new form of channel conflict, which is a focus of this article. We consider a setting in which a marketplace firm operates an online marketplace through which retailers can sell their products directly to consumers. We consider a single retailer, who currently sells its product only through its own website, but who may choose to contract with Amazon to sell its product through the marketplace system. Selling the product through the marketplace expands the available market for the retailer, but comes at some expense, e.g., a fixed participation fee or a revenue sharing requirement. Thus, a key question for the retailer is whether she should choose to sell through the marketplace system, and if so, at what price. We analyze the optimal decisions for both the retailer and the marketplace firm and characterize the system equilibrium.     

Vertical Integration under Competition: Forward,Backward, or No Integration?

We consider two competing supply chains, each consisting of supplier, a manufacturer, and a retailer. The suppliers exert effort to improve product quality, and the retailers sell products competitively. Each manufacturer chooses one of the three strategies: forward integration, backward integration, or no vertical integration. We seek for a subgame perfect Nash equilibrium and study the resulting market structure. Moreover, we characterize the effect of vertical integration on profitability, product price, and quality in a competitive setting. Existing literature has shown that, when manufacturers consider only forward integration, they may choose not to vertically integrate in equilibrium. In contrast, we find that, when both forward and backward integration options are considered, disintegration cannot be an equilibrium outcome. In this case, both manufacturers either forward or backward integrate, and the degree of product perishability, cost of quality, and how much consumers value quality are critical for the chosen direction of integration. Furthermore, competition increases attractiveness of backward integration relative to forward integration. We show that, while integrating backward unilaterally is always beneficial, unilateral forward integration can harm a manufacturer's profitability. Finally, vertical integration can result in a better quality product sold at a lower price.     

最优交易策略对交易持续期的影响

构建一个纯流动市场交易动态策略模型。假设交易者按Poisson过程到达市场,交易者根据其私人估值及市场状态对限价指令的收益做预期,通过最大化其收益确定所提交指令的类型(限价指令或市价指令)。模型发现,虽然交易者到达市场的时间间隔相互独立,但交易持续期却受前一期的交易策略影响:买(卖)指令的提交将增加下一期卖(买)交易持续期的期望值,减小下一期买(卖)交易的持续期的期望值。因而,交易间的自相关性是依据最优交易策略所内生的性质,与知情交易无关。     

The Economic Value of Market Information for Farmers in Developing Economies

In developing countries, farmers lack information for making informed production, manufacturing/selling decisions to improve their earnings. To alleviate poverty, various non‐governmental organizations (NGOs) and for‐profit companies have developed different ways to distribute information about market price, crop advisory and farming technique to farmers. We investigate a fundamental question: will information create economic value for farmers? We construct a stylized model in which farmers face an uncertain market price (demand) and must make production decisions before the market price is realized. Each farmer has an imprecise private signal and an imprecise public signal to estimate the actual market price. By examining the equilibrium outcomes associated with a Cournot competition game, we show that private signals do create value by improving farmers' welfare. However, this value deteriorates as the public signal becomes available (or more precise). In contrast, in the presence of private signals, the public signal does not always create value for the farmers. Nevertheless, both private and public signals will reduce price variation. We also consider two separate extensions that involve non‐identical private signal precisions and farmers' risk‐aversion, and we find that the same results continue to hold. More importantly, we find that the public signal can reduce welfare inequality when farmers have non‐identical private signal precisions. Also, risk‐aversion can dampen the value created by private or public information.     

THE POLITICAL ECONOMY OF FLEXICURITY

We document the presence of a trade‐off in the labor market between the protection of jobs and the support offered to unemployed people. Different countries’ locations along this trade‐off represent stable political‐economic equilibria. We develop a model in which individuals determine the mix of job protection and support for the unemployed in a political environment. Agents are heterogeneous along two dimensions: employment status (insiders and outsiders) and skills (low and high). Unlike previous work on the political economy of labor market institutions, we emphasize the role of job protection and unemployment benefits in the wage‐setting process. A key implication of the model is that flexicurity configurations with low levels of job protection and high levels of support to the unemployed should emerge in the presence of a highly educated workforce. Panel regressions of countries’ locations along this institutional trade‐off are consistent with the implications of our model.     

(Un)equal Educational Opportunities and the Labor Market: A Theoretical Analysis

This paper intends to study the effects of public school quality offer on the labor market performance. With this objective in mind, we build a matching model for the labor market in two sectors: schooled and non‐schooled. The skilled segment of the economy is endogenous and composed of a continuum of workers who differ in the quality of the school attended. We show that there is a trade‐off between the quantity and the quality of education and that a reduction in schooling costs increases school enrollment rates. However, it adversely reduces the job creation dynamics in the skilled sector, due to the Composition Effect. We also verify that a first order improvement in school quality distribution may generate an increase in the schooling rate and a greater job vacancy creation in the skilled sector with no negative effects on the unskilled sector.     

Strategic Liquidity Provision in Limit Order Markets

We characterize and prove the existence of Nash equilibrium in a limit order market with a finite number of risk‐neutral liquidity providers. We show that if there is sufficient adverse selection, then pointwise optimization (maximizing in p for each q) in a certain nonlinear pricing game produces a Nash equilibrium in the limit order market. The need for a sufficient degree of adverse selection does not vanish as the number of liquidity providers increases. Our formulation of the nonlinear pricing game encompasses various specifications of informed and liquidity trading, including the case in which nature chooses whether the market‐order trader is informed or a liquidity trader. We solve for an equilibrium analytically in various examples and also present examples in which the first‐order condition for pointwise optimization does not define an equilibrium, because the amount of adverse selection is insufficient.     

Inventory Sharing in the Presence of Commodity Markets

This study investigates the value of inventory sharing in the presence of spot and forward markets. We consider a multi‐period setting where two firms process a common commodity to meet stochastic demands. They can buy and sell the commodity through both the spot and forward markets. They can also share the commodity if one has leftover inventory while the other has excess demand. We first characterize the equilibrium strategies of the two firms. Our analysis reveals that in such a context, the value of inventory sharing is low when the forward price is directly used to value the sharing transactions. We then develop a structured trans‐shipment price scheme that uses a linear combination of the spot and forward prices. We show that this method can substantially increase the value of inventory sharing. Our analysis also reveals that in the presence of liquid spot and forward markets, the value of inventory sharing mainly results from the difference of the transaction costs, and it increases if the market in which firms operate becomes more competitive.     

The Impact of Trade on Intra‐Industry Reallocations and Aggregate Industry Productivity

This paper develops a dynamic industry model with heterogeneous firms to analyze the intra‐industry effects of international trade. The model shows how the exposure to trade will induce only the more productive firms to enter the export market (while some less productive firms continue to produce only for the domestic market) and will simultaneously force the least productive firms to exit. It then shows how further increases in the industry's exposure to trade lead to additional inter‐firm reallocations towards more productive firms. The paper also shows how the aggregate industry productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a benefit from trade that has not been examined theoretically before. The paper adapts Hopenhayn's (1992a) dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the paper provides an extension of Krugman's (1980) trade model that incorporates firm level productivity differences. Firms with different productivity levels coexist in an industry because each firm faces initial uncertainty concerning its productivity before making an irreversible investment to enter the industry. Entry into the export market is also costly, but the firm's decision to export occurs after it gains knowledge of its productivity.