Identical Buyers Research Articles

Macro shocks cause equilibrium price dispersion

Price dispersion is shown to arise when demand is stochastic, ex-ante identical competitive firms set price prior to the realization of uncertainty and ex-ante identical buyers cannot switch sellers if rationed.

Equivalence of canonical matching models

This paper offers expected revenue and pricing equivalence results for canonical matching models. The equivalence of these models is centered on the assumption that there are large numbers of buyers and sellers, and the contact decisions of buyers to sellers are made independently. Therefore, the distribution of buyers to sellers is approximated by the Poisson distribution. The list of canonical matching models includes the models developed by Burdett and Judd (1983), Shimer (2005), and McAfee (1993). In the Burdett and Judd model, buyers post prices and the equilibrium features price dispersion because identical buyers play mixed strategies. In the Shimer model, sellers post a vector of prices corresponding to different buyer types. In equilibrium, all identical buyers pay the same price. In the McAfee model, equilibrium pricing is determined by simple second price auctions. McAfee's model also features price dispersion because the number of bidders at each auction is stochastic.

3D Printing of Spare Parts Via IP License Contracts

Additive manufacturing (AM), also known as 3D printing, has the potential to shift supply chains from global networks that rely on centralized production with traditional manufacturing technologies to largely digital networks with decentralized, local 3D printing, i.e., digital inventory. One type of firm that is particularly well positioned to drive this transition are original equipment manufacturers (OEMs), who design and produce capital goods. In this paper we propose that the OEM acts as an intellectual property (IP) licensor by selling spare parts designs, rather than physical spare parts. With these designs a buyer can print spare parts locally at much shorter lead times and at lower setup costs. We consider both an OEM who serves multiple identical buyers, and an OEM who serves two non-identical buyers. For both cases we characterize the optimal IP license contract. This determines which customers opt for the IP license channel and which remain in the traditional centralized sales channel, thus creating insights into the degree to which a supply chain decentralizes. We numerically show this to occur in a surprisingly large number of cases and we observe significant profit increases for OEMs who adopt this new business model. Our results thus show that IP licensing by OEMs can become a major enabler in the transition to digital networks with decentralized 3D printing.

Bilateral trading and incomplete information: Price convergence in a small market

We study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. In addition to this seller with private information, there are two identical buyers and another seller, whose valuation is commonly known to be in between the two possible valuations of the seller with private information. We consider an infinite horizon game with simultaneous one-sided offers and simultaneous responses. We construct one particular PBE of the game and show that, as the discount factor goes to 1, prices in all transactions converge to the same value. We then show that this is the case with any stationary equilibrium of the game. That is, the asymptotic outcome is unique across all stationary equilibria.

False Diagnoses: Pitfalls of Testing for Asymmetric Information In Insurance Markets

The widely applied ‘positive correlation test’ concludes that there is symmetric information in an insurance market if observationally identical buyers of high and low cover contracts have the same loss rate. As standard assumptions imply that only full‐cover contracts are bought when information is symmetric, a contradiction arises. The existence of a variety of contracts can be reconciled with symmetric information by claim‐processing costs but existing tests are then shown to fail. Ignoring the nature of loading factors may also cause recent studies to mismeasure the welfare costs of asymmetric information but these errors can be rectified.

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.

Nonexclusive competition under adverse selection

Consider a seller of a divisible good, facing several identical buyers. The quality of the good may be low or high, and is the seller’s private information. The seller has strictly convex preferences that satisfy a single-crossing property. Buyers compete by posting arbitrary menus of contracts. Competition is non-exclusive in that the seller can simultaneously and secretly trade with several buyers. We fully characterize conditions for the existence of an equilibrium. Equilibrium aggregate allocations are unique. Any traded contract must yield zero proflt. If a quality is indeed traded, then it is traded e‐ciently. Depending on parameters, both qualities may be traded, or only one of them, or the market may break down completely to a no-trade equilibrium.

Non-Exclusive Competition Under Adverse Selection

Consider a seller of a divisible good, facing several identical buyers. The quality of the good may be low or high, and is the seller's private information. The seller has strictly convex preferences that satisfy a single-crossing property. Buyers compete by posting arbitrary menus of contracts. Competition is non-exclusive in that the seller can simultaneously and secretly trade with several buyers. We fully characterize conditions for the existence of an equilibrium. Equilibrium aggregate allocations are unique. Any traded contract must yield zero pro t. If a quality is indeed traded, then it is traded efficiently. Depending on parameters, both qualities may be traded, or only one of them, or the market may break down completely to a no-trade equilibrium.

Price Dispersion with Directed Search

We model a market where identical buyers direct their search to identical capacity-constrained sellers. Sellers cannot fully commit to the list price so strategic bargaining may determine the sale price. We study search and pricing behavior in symmetric equilibrium. Sale prices exhibit equilibrium dispersion as they respond naturally to local demand conditions. Uncoordinated search decisions lead to equilibrium demand heterogeneity, so sellers realizing large demand bargain prices up. We characterize the sale price distribution parametrically, studying how different commitment limitations and market features affect pricing and surplus shares. We also determine endogenously

An Experiment on the Core

Each of n ≥ 1 identical buyers (and m ≥ 1 identical sellers) wants to buy (sell) a single unit of an indivisible good. The core predicts a unique and extreme outcome: the entire surplus is split evenly among the buyers when m > n and among the sellers when m < n; the long side gets nothing. We test this core conjecture in the lab with n + m = 3 or 5 randomly rematched traders and minimal imbalances (m = n ± 1) in three market institutions. In the standard continuous double auction, the surplus indeed goes overwhelmingly towards the short side. The DA-Chat institution allows traders to have cheap talk prior to the double auction, while the DA-Barg institution allows the long siders to negotiate enforceable profit sharing agreements while trading. Despite frequent attempts to collude and occasional large deviations from the core prediction, we find that successful collusion is infrequent in both new institutions. A disproportionate fraction of the successful collusions are accompanied by appeals to fairness.

Multi-player bargaining with endogenous capacity

We study equilibrium prices and trade volume in a market with several identical buyers and a seller who commits to an inventory and then offers goods sequentially. Prices are determined by a strategic costly bargaining process with a random sequence of proponents. A unique subgame perfect equilibrium exists, characterized by no costly delays and heterogeneous sale prices. In equilibrium constraining capacity is a bargaining tactic the seller uses to improve a weak bargaining position. With capacity constraints, sale prices approach the outcome of an auction as bargaining costs vanish. The framework provides a building block for price formation in models of equilibrium search with multilateral matching, and offers a rationale for the adoption of single-unit auctions with fixed reservation price.

A study of quantity discount pricing models with different ordering structures: Order coordination, order consolidation, and multi-tier ordering hierarchy

In this paper, we study quantity discount pricing models with different ordering structures in a system consisting of a single supplier and heterogeneous buyers. We start with the case where the ordering schedule of the buyers is not coordinated and determine the optimal parameters that minimize the joint (system) costs. Later, we consider the case where the discount policy is structured such that the buyers are encouraged to coordinate the timing of their orders. For the case of identical buyers, we show that order coordination always leads to a reduction in the system costs. However, with heterogeneous buyers, we derive the sufficiency conditions that determine when “order coordination” would be preferable. A numerical example illustrating the benefit of “order coordination” is also presented. Then, we consider the case when the buyers place a combined (single) order with the supplier (referred to as “order consolidation”). It is shown that if the supplier offers the same discounted price (the price offered when the buyers coordinate their orders), the buyers would prefer “order consolidation” over “order coordination”. However, for the supplier, conditions derived indicate that the supplier would prefer that the buyers coordinate their orders. Finally, we consider the case of a multi-tier ordering hierarchy where only one of the buyers (for example, a major wholesaler) places an order from the supplier. The remaining buyers, in turn, place orders only from the major buyer. Optimal ordering decisions are again determined and comparisons made with the case of “order consolidation”.

Buyer experimentation and introductory pricing

We study the pricing decisions of a monopolist seller in a two-period model in which buyers and the seller are all uncertain about a good’s quality. We assume that buyers not only learn from experience, but also may experiment, that is, increase the amount of information by consuming more. We define an introductory price to be a first period equilibrium price lower than that which maximizes period 1 profit. The motivation for introductory pricing is that, under certain conditions, the seller prefers its buyers to be better informed about quality. A lower initial price increases consumption and hence information. We consider two versions of the model: identical buyers with a public signal of quality; heterogeneous buyers who each receive a private quality signal.

Ricardian Equilibrium with Stochastic Free Entry

The standard Ricardian model of competition has a fixed number of firms, each with limited capacity and differential exogenous costs or qualities. In this paper, we introduce a real entry process by formulating a multistage Ricardian equilibrium model with free entry and stochastic product qualities and costs. The set of firms and their qualities and costs are determined by an equilibrium dynamic entry process in which an unlimited number of potential entrants face identical investment costs and prospects. In the first stage, each firm sequentially chooses whether or not to undertake a risky investment that determines its quality and cost. The process continues until no more firms wish to invest. In the second stage, the firms compete to sell their limited capacity to a fixed number of identical buyers. The resulting Ricardian stochastic free entry equilibrium has a number of interesting properties. Firms invest as long as the active (i.e., worst sold) seller's quality (or cost) does not meet a critical threshold that does not depend on the realizations of the other sellers or the number of units demanded. There are two possible equilibrium market structures. One structure involves excess sellers in which prices are determined by the cost and quality of the (i.e., best unsold) seller. The other structure involves the number of investing potential entrants just equal to the number of units demanded, and sellers charging prices equal to the buyers' value. Regardless of the market structure, the entry process and equilibrium are socially optimal. Surprisingly, demand increases either have no effect on prices or, more generally, lead to lower prices. Restricting sales by sellers similarly cannot lead to higher prices because such supply restrictions induce entry investment that continues until a new entrant replaces the unit that was withheld from the market. In fact, it generally leads to lower prices. However, warehousing the marginally inactive (best unsold) unit is a profitable method of raising prices because it does not induce entry. In the limiting case of a large number of small sellers, the model nicely illustrates the distinction between short and long run competitive equilibrium, and the expected price converges to a long run supply price.

The Long Side of the Market and the Short End of the Stick: Bargaining Power and Price Formation in Buyers', Sellers', and Balanced Markets

The determinants of bargaining power and price formation in a dynamic exchange market where new traders enter randomly over time are studied. When agents on the long side of the market possess the option to wait for the arrival of future partners, the terms of trade in the spot market must honor the value of this option. The equilibrium terms of trade are expressed in intuitive closed-form equations that highlight the distinct influences of short-run spot-market conditions and long-run market demographics. I. INTRODUCTION Few concepts in economics are as intuitive as the idea that traders on the long side of a market wind up holding the short end of the stick. That is, they receive little or none of the gains from trade. Consider, for instance, the classic setting in which b identical buyers each with unit demands for an indivisible homogeneous good face s identical sellers each with one unit of the good for sale. It is well-known that in a broad class of one-shot trading games, all of the surplus in this setting goes to the short side of the market; in equilibrium. That is, if b s, buyers bid the price up to their reservation value. Often, it is only when b = s that market institutions (the rules of the game) have any bearing on the equilibrium division of surplus. This classic result is somewhat brittle because of the discontinuity in the terms of trade when moving from positive to negative levels of excess demand. Its logic is familiar, however, from Bertrand competition, and it is very compelling. The option value to an agent frozen out of a trade in a one-shot market game is his reservation payoff of zero. Any outcome that confers nonzero surplus to a long-side agent cannot be sustained in equilibrium, because all of the long-side agents who would otherwise be frozen out possess a strict incentive to undercut.

Enhancing bargaining power with most-favored-customer pricing

A monopolist faces a finite sequence of identical buyers and negotiates with each buyer individually. Most-favored-customer pricing allows the firm to exploit its position as the repeat player in the game and extract more of each buyer's surplus.

An Operational Model for Spatial Price Theory

This paper uses the basic properties of a general model of spatial pricing and distribution to establish an operational model that is free of many standard restrictive assumptions. In particular, the landscape viewed is not subject to the usual homogeneity assumptions of (1) an even distribution of identical buyers and (2) constant freight rates. Rather, heterogeneous distributions and demands of varying forms are assumed. The operational form that is constructed herein would enable empirical testing and application over a broad range of industries and countries. A few case examples are included in the paper to help characterize the data that empirical studies could discover in a world of heterogeneities among buyers and landscapes.

A Simple Model of Equilibrium Price Dispersion

This paper demonstrates that price dispersion can exist even within the context of a very simple model. Identical buyers with elastic demand curves sample sequentially from a known price distribution, at a fixed cost per observation. Firms are assumed to be perfectly informed of buyers' reservation prices and demand functions. Given the firms' distribution of marginal costs, firms' behavior as monopolistic competitors results in their offering a distribution of prices which is consistent with expected utility maximization by buyers and with expected profit maximization by sellers.