The matching problem (and inventories) in private negotiation.

Many transactions in the food and fiber sector are conducted through private negotiation. A buyer and a seller, or respective agents, meet and haggle over price and possibly other features of the deliverable. The majority of fed cattle procurements (53.9% of the total) in 2003, for example, were privately negotiated (Ward 2005). At another level of the beef supply chain, retailers bilaterally bargain with packers for boxed beef. In many bilateral trading environments, the seller must have inventory on hand before negotiations begin; production comes in advance of trading. This is a characteristic of fed cattle, other agricultural commodities, and a number of processed food markets. Advance production can create a risk of inventory loss, particularly for perishable commodities/products (Menkhaus, Phillips, and Bastian 2003). (1)

There can be asymmetry in the number of negotiating buyers and sellers in a bargaining environment. There may be more sellers than buyers, or vice versa, which can create a matching problem for traders. Some agents may have difficulty finding a trading partner, because the potential partner is negotiating with someone else, or their current marginal willingness to buy or sell does not permit any gains from further negotiation. Sellers facing limited matches and holding large inventories could be forced to trade at deep discounts or be left with unsold units at the end of a trading session. (2) Trading agents increasingly have engaged in selected vertical arrangements to overcome the matching problem. While such coordination between firms may better align incentives and reduces transaction costs for the vertically linked agents, finding a willing buyer or seller can become even more difficult for firms not vertically controlled. Further, consolidations in food retailing and processing industries have resulted in a few large firms as buyers or sellers, exacerbating asymmetry in the bargaining environment. This study examines laboratory market outcomes when there is advance production and limited matches between different numbers of buyers and sellers.

Menkhaus et al. (2003) have conducted private negotiation experiments without advance production. Buyers and sellers were randomly matched in three bargaining rounds per trading period. The authors observed prices in private negotiation trading near the predicted competitive price at the intersection of supply and demand, and very near those observed in a double auction. The privately negotiated quantity, however, was below the level predicted by the competitive model, reflecting some loss in total surplus. (3) Perishable inventories put sellers under increased pressure to sell. Risk-averse sellers reduce this pressure by producing less. Double auction trading with advance production, when compared to a double auction without this feature, results in significantly higher prices and less quantity traded, although the latter is still within the predicted range from the competitive model (Phillips, Menkhaus, and Krogmeier 2001). Also, an English auction with advance production results in prices above and quantities traded below those levels predicted by the competitive model and resulting favorable earnings to sellers (Menkhaus, Phillips, and Bastian 2003). Previous research suggests double and English auctions coupled with advance production generally favor the seller.

As shown below, market outcomes can reverse and favor the buyer when traders privately negotiate for inventory in stock. Advance production and private negotiation trading with limited bargaining rounds give buyers monopsony power in the last rounds, which can extend backward into earlier bargaining rounds. We believe this is due to the matching problem. Sellers lose their advantage in private negotiation trading, as compared to double and English auctions. Relatively few buyers reinforce monopsony power. A relatively small number of sellers can measurably counteract the bargaining power of buyers.

Theoretical Considerations

In this section, we consider alternative perspectives on the behavior of agents in privately negotiated trading with advance production. This discussion provides baselines from which to judge observed bargaining outcomes.

Inventories and Cournot Behavior

A market environment in which sellers first make a production decision and then put goods up for sale at an auction is the purest form of a Cournot market structure. The choice variable at the production stage is quantity, and market price is determined in the second stage of the game through an auctioneer. The stylized story is that the auctioneer sells all production in the second stage. Auctions are considered to be an efficient means of equating supply and demand. Kreps and Scheinkman (1983) prove the generality of this construct as long as there is advance production. Even in a Bertrand game, if production precedes price competition, limited inventories generate prices above marginal cost and "yield Cournot outcomes." A main point of the Kreps and Scheinkman (1983) work is that inventory requirements have a very powerful influence on market outcomes. Davis (1999) finds a shift from the competitive equilibrium to the Cournot outcome when sellers first make binding production commitments and then post prices (see Goodwin and Mestelman [2006] for a recent discussion of inventories and posted-offer markets). In our experiments, there is production and then a bilateral bargaining stage. For sellers as a group, we can solve for the Cournot equilibrium, as presented later, and use this as a point of comparison in our data analysis.

Limited Matches and Backward Induction: A Monopsony Story

Imagine different sellers and buyers matched n times following a production period. At the beginning of the period, sellers make an output decision and inventory is in stock. Inventory cannot be carried over to the next production period, a characteristic of perishable products, or products that become outdated from model changes or new technology. The sellers have the opportunity to sell multiple units during the n rounds of matches with buyers in private negotiation trading, but excess inventory becomes worthless at the end of the nth negotiating round. In the last round of bargaining, a buyer has the incentive to bid and pay virtually zero for all stock. Through backward induction, this means that zero should be paid in the n - 1 round, then for the n -2 round, and so on for all negotiation rounds. The predicted Nash equilibrium price is zero for a single production period.

[FIGURE 1 OMITTED]

In a game with production in multiple periods, however, this cannot be an equilibrium, because sellers will not produce in future periods. (4) A buyer in a multi-period game with n bargaining rounds in each period seeks to maximize surplus. If there is no price discrimination and the buyer pays a uniform price, buyer surplus is maximized where marginal factor cost intersects the demand schedule and price is from the supply schedule. Price and quantity traded are determined as if the buyer has monopsony control in the market. We use this as the stylized multiple production period Nash equilibrium. (5)

In a trading environment like that constructed in our computer laboratories, with several buyers and sellers, an individual agent faces a matching risk. Late random matches may pair a buyer with a seller who has no inventory for sale. In a less extreme case, traders may be disadvantaged due to the relative difference between their respective marginal benefits and marginal costs. As a result, traders have an incentive to trade early in a production period, and this may dilute some of the buyer's bargaining power that results from advance production. Buyers, wishing to avoid a late mismatch, will bid the price above the monopsony level. The matching problem can benefit sellers, because it damages the control of buyers in the late bargaining rounds of trading. As the number of bargaining rounds increases, the probability of mismatches toward the end of a production/trading period increases, and buyers have less control over price. In this context, we expect price to be more competitive and the bargaining advantage of buyers in private negotiation trading with advance production to dissipate.

To summarize, we believe three market equilibria can be useful in predicting price and quantity outcomes in the bargaining environment we construct. They are the competitive, Cournot, and monopsony solutions. Behavior will be different depending on the relative numbers of buyers and sellers and the number of matches. Laboratory market results will provide evidence to validate appropriate theory in this market environment.

Experimental Design and Laboratory Procedures