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

The experimental design captures the matching problem in private negotiation trading with advance production (see figure 1 for the organization of an experimental session). Each trading period begins with a production decision, followed by several rounds of bargaining for price. A baseline treatment has four buyers and four sellers to be randomly matched/paired at the beginning of each of five bargaining rounds. Random re-matching at the beginning of each bargaining round can result in the same buyer and seller being matched in a subsequent round. Buyers and sellers are randomly and anonymously matched in order to avoid the formation of agreements and reputation building among agents. Three other treatments make matching more difficult. Reducing the number of bargaining rounds from five to three in the experiments, as well as creating asymmetry in the number of buyers or sellers in the market, both increase the matching problem. Four treatments make up the experimental design (table 1).

Designated as 5M, the baseline treatment has four buyers and four sellers with five matches during each of 20 trading periods. Treatment (3M) reduces the number of matches from five to three, again using four buyers and four sellers. A third treatment (2B5M) reduces the number of buyers to two, who are randomly matched with two of the four sellers during five bargaining rounds. Two sellers, therefore, did not trade during each of the bargaining rounds. Hence their expected number of matches is 2.5, while buyers have five matches. The final treatment (2S5M) consists of two sellers randomly matched with four buyers for five bargaining rounds per trading period. In this treatment, two buyers did not trade during each of the bargaining rounds. The 2S5M treatment is designed to provide insight into the amount of bargaining power sellers might gain as they become more concentrated, e.g., through a bargaining association or cooperative. The expected number of matches is 2.5 for buyers and five for sellers.

Subjects were recruited, primarily from undergraduate business and economics classes. A list of participant names was kept to minimize the chances of subjects participating more than once in the experiments. (6) The participants randomly drew a slip of paper that designated them as either a buyer or seller when they entered the computer laboratory. Buyers and sellers were asked to sit in separate sections of the room and each participant was seated in a different row. This procedure minimized visual interaction of participants. The instructions for the experiment were then read and followed by a practice session, which included as many production/trading periods as were necessary for all participants to become familiar and comfortable with the procedures (typically two to three periods). After the production decision, there were one-minute bargaining rounds (three or five) during which a buyer and seller exchanged "units" from a computer station through private, bilateral negotiation. Buyers were supplied with redemption values for units they could purchase. Sellers were given production costs for units they could produce and then sell. Unit values and costs were different in the practice session than in the actual experiment. Participants were told to keep their values and costs private. An artificial currency called "tokens" was used, with an exchange value of one cent per token. The unit values and unit costs, which were the same for each of the four buyers and four sellers, respectively, are presented in table 2. Each of the four treatments was replicated three times, i.e., there were three separate sessions of twenty trading periods for each treatment. Participants were unaware that trading would be terminated at the end of period twenty and also were not informed about how long the session would last.

Buyers waited while sellers made their production decisions. Once all sellers completed a production decision, which was private information, the trading began. For each one-minute bargaining round, buyers and sellers sequentially traded as many units as they could to make money. The matched buyer/seller pairs made bids and offers, respectively, until bids and offers were equal, or until the buyer or seller accepted the existing bid or offer. Following each trading period an individual's earnings were posted on their computer screen. Buyers earned the sum of the difference between what they paid for a unit ([P.sub.i]) and the given redemption value for that unit, i.e.,

(1) BuyerEarnings

= [n.summation over (i=1)](Redemption[Value.sub.i] - [P.sub.i])

where j = number of units purchased. Sellers earned the sum of the difference between unit price ([P.sub.i]) and its unit cost, i.e.,

(2) Seller Earnings = [k.summation over (i=1)] ([P.sub.i] - Unit[Cost.sub.i])

where k = number of units produced. If sellers did not trade a unit that was produced, [P.sub.i] = 0 and the cost of the unit was lost. There was no inventory carryover. Earnings accumulated over the sequence of trading periods and were displayed on the individual computer screens at the end of each period. Participants could view only their own information. Average participant earnings across all treatments were about $29 for 1 1/2 to 2 hours of participation.

Each participant was given an initial endowment of $7.00 or 700 tokens at the beginning of each session. The initial endowment was necessary because sellers incurred costs associated with advance production prior to being given the opportunity to earn profit from sales. Another concern was that the initial token balance be large enough to preclude the possibility of bankruptcy early in the session for individual sellers. This initial balance was given to both buyers and sellers in order to maintain symmetry.

The cost schedule for sellers ranged from thirty tokens for the first unit produced to a hundred for the eighth unit produced, as seen in table 2, for treatments 1 and 2. Redemption values for buyers ranged from 130 tokens for the first unit purchased to sixty tokens for the eighth unit in these two treatments. In treatment 3 (with two buyers), each buyer was able to buy sixteen units and the unit values were 130 tokens for the first two units, 120 for the third and fourth units, etc. Similarly, in the fourth treatment (with two sellers), each of the two sellers can produce up to sixteen units each. The unit cost schedule had two units costing thirty tokens, two units at forty tokens, etc. These schedules roughly (due to their discrete nature) translate to the individual supply schedule p = 25 + 10q and the individual demand p = 135 - 10q.

Horizontally summing the unit values and unit costs for the four buyers and four sellers results in a predicted competitive equilibrium price of eighty tokens and quantity twenty of to twenty-four units. The Cournot solution (four sellers) is 86.11 tokens and 19.56 units traded. The predicted monopsony price is sixty tokens with sixteen units traded. These serve as base values in the analysis that follows.

Methods of Analysis and Results from Laboratory Markets

Data collected from the laboratory markets include quantities traded and trade prices. Descriptions of the characteristics of each of these market outcomes over the twenty trading periods and four primary treatments are provided by means of a graphical analysis and a convergence model (Noussair, Plott, and Reizman 1995). The former offers a description of the general tendencies and the latter allows for tests of statistical inferences regarding differences between convergence levels across treatments relative to baseline predictions and between treatments. The following general convergence model is estimated for quantities traded and prices, [Z.sub.i], from the alternative treatments using the alternative base category predictions:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [Z.sub.it] = average sale price (or units traded) across the replications of the treatment and all trades for each of the trading periods in cross-section treatment i; [B.sub.0] = the predicted convergence level of the dependent variable for the base category (competitive, Cournot, or monopsony prediction); [B.sub.1] = predicted starting level of the data for the base category; t = trading periods 1, ..., 20; [D.sub.j] = dummy variable separating the j treatments and [u.sub.it] = error term. Six equations were estimated; there is a price and trade equation for each of the three base categories. The base price (tokens) and quantity trade (units) values for the competitive, Cournot, and monopsony equilibria are, respectively, 80 and 20, 86.11 and 19.56, and 60 and 16, as previously reported.

The dummy variables ([D.sub.j]) take on the value of one when the dependent variable is from the jth treatment (3M, 5M, 2B5M, and 2S5M) and are otherwise zero. For the base, the convergence level of the dependent variable is given by [B.sub.0], while [B.sub.1] is the estimated origin (starting level) of the time series. If t = 1, then the value of the dependent variable is equal to [B.sub.1] for the base treatment. As t gets large, the weight of [B.sub.1] is small, because 1/t approaches zero, while the weight of [B.sub.0], (t - 1)/t approaches 1. The base treatment holds [B.sub.0] and [B.sub.1] fixed, but these values are adjusted by [[alpha].sub.j] and [[GAMMA].sub.j], respectively, for other treatments. In this study, the estimated [[alpha].sub.j] (the asymptote coefficients) are the parameters of interest, because they measure how trade or price convergence levels for the treatments deviate from the base category prediction (table 3). (7)

Observations generated over several time periods may be serially correlated and heteroscedastic. Data also may be contemporaneously correlated between cross-sections due to the same unit values/costs being used by subjects across alternative treatments. The Parks (1967) method was used to estimate equation (1). The use of the Parks method allowed us to take account of the unique statistical problems resulting from the panel data sets that consist of time series observations on each of the several cross-sectional units generated in our experiments, along with base category predictions. (8)

Quantities Traded

The 5M treatment exhibits the greatest number of units traded, slightly more than seventeen units and consistently above the monopsony level, followed by the 3M treatment; see figure 2. Treatments in which the buyers or sellers are consolidated consistently show the fewest units traded. As discussed later, trades in these two treatments converge to levels that are not significantly different but are statistically different from the 3M and 5M treatments (table 3). Quantities traded in all treatments are below the predicted competitive and Cournot levels, and each treatment, as shown in figure 2, generally reflects a pattern with small variations across the trading periods.

[FIGURE 2 OMITTED]

Estimated convergence levels for trades in all treatments are low, relative to base values. They are significantly less than the predicted competitive and Cournot quantities in all treatments, and are generally below the monopsony prediction, except in the 5M treatment, which converges to a quantity slightly greater than the monopsony level (table 3). The estimated convergence levels for trades for the 5M and 3M treatments, between which the effects of limited matching can be isolated, are about 17.30 and 14.60, respectively, and are significantly different. This is a simple, but important, observation. Less access between the bargaining agents when there is advance production decreases production and the quantity traded. In this particular instance, a 40% decrease in matches resulted in a 15% decrease in trades; this occurred with no change in the basic supply and demand conditions. Lower production/trades also reflect the perceived higher costs associated with the risk of inventory loss.

The greatest differences from the base trade levels are for the 2B5M and 2S5M treatments, with estimated convergence levels of about 12.70 and 13.20 units, respectively. These levels are not significantly different from each other but are significantly lower than 5M and 3M treatment levels, and are significantly below the monopsony level of sixteen units. This result reflects the impact of fewer matches for sellers or buyers resulting from concentrated markets on either the buyer side or seller side. Buyers and sellers appear equally capable of exploiting bargaining power due to their relatively small number. Limited access in a bargaining environment that arises through increased concentration can have a substantial impact on trades. Taking the market from four to two sellers or four to two buyers (each with five matches) reduces estimated convergence quantities from 17.28 to levels near 13 units. This represents about a 24% decrease in trades. Based on the relative magnitudes of the estimated differences from the respective predicted levels, the monopsony model predicts trades in all treatments more accurately than the competitive or Cournot models. The differences from the monopsony equilibrium level of sixteen units are all significant, however.

The highest fractions of all trades occur in the first and second bargaining rounds as reported in table 4. Trading periods sixteen to twenty are used for illustration. Subjects have the most experience in these trading periods. This pattern of trades indicates the desire by buyers and especially sellers to avoid later mismatches. The lack of transactions late in a trading period arises from an absence of viable bargains. About 81% of all trades are executed in the first three rounds of the 5M treatment. When the number of buyers is reduced (2B5M), 77.83% of trades occur in the first three rounds, as compared to 68.71% when the number of sellers is reduced (2S5M). The market containing two sellers has 15.34% of the trades occurring in the fifth round, which is the highest among the treatments with five matches. This last result suggests that risk from holding inventory is not as severe for sellers when they are relatively concentrated. Sellers do not produce additional units and are more patient in this environment (table 3). The two sellers are in a position to exercise monopoly power facilitated by the limited access to them.

At the end of a trading period any unsold inventories (charged at the unit costs) become a sunk cost to sellers. These losses and the potential for losses put pressure on sellers to accept lower prices in the current period and produce less in future periods. An analysis of unsold inventory for periods sixteen through twenty reveal an average of unsold inventory of 0.07 units per period for the 5M treatment, 0.66 units for the 3M treatment, 1.73 units for the 2BSM treatment, and 0.17 units for the 2S5M treatment (see figure 3). The highest level of loss occurs when there are just two buyers with the next highest average number of unsold units occurring during the 3M treatment. It is possible that buyers in the 2B5M treatment were establishing a reputation early on for letting inventory "spoil"--opportunistic behavior resulting in the classic hold-up problem. These unsold inventory numbers reflect levels of matching risk faced by sellers. It was greatest when either the number of bargaining rounds or number of buyers was reduced. Comparing the average units lost between the early and later trading periods generally suggests more units were lost in early periods than later. Experience did matter in these bargaining treatments (table insert--figure 3).

Prices

Figure 4 summarizes average transaction prices for each treatment. Most noticeable is that prices in the buyer concentrated treatment (2B5M) are much lower than prices in other treatments, and exhibit convergence levels significantly lower than in other treatments (table 3). Toward the end of the experimental session prices in the 2B5M treatment are around sixty-five tokens, while in the other treatments they are in the range of seventy-five to eighty tokens. The concentration of buyers brings a substantial reduction in negotiated prices. Noteworthy is that prices are consistently lower in the 3M treatment relative to the 5M treatment, with convergence levels statistically different. A general reduction in the number of matches reduces trade prices. Hence both quantities and prices fall in going from the 5M to 3M environment. Generally higher prices are observed in the 5M and 2S5M market environment, and prices in these two treatments tend toward, or vary about, the competitive equilibrium level of eighty tokens. Quantities sold in the 2S5M are lower, so the total market surplus will be lower.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The estimated convergence price increases by 4.70 tokens when the number of bargaining rounds increases from three to five (3M to 5M treatment) per trading period and moves to within 2.36 tokens of the competitive equilibrium price of eighty tokens (table 3). Price tends toward the competitive level as the matching problem decreases for both buyers and sellers. The risk of inventory loss also diminishes with more matches, as gleaned from the table insert in figure 3. Thus, the overall convergence patterns show that by going from three to five matches, trades and prices increase. Trades rise from 14.61 to 17.28 units (an 18% increase) and prices rise 6.4%, from 72.94 to 77.64 tokens.

Prices are most depressed in the 2B5M treatment, exhibiting an estimated convergence level of just over sixty-two tokens, the statistically lowest among all treatments and near the monopsony level of sixty tokens. Few expected matches for sellers put buyers in an advantageous bargaining position in private negotiation trading with advance production. Compared to the 5M treatment, prices in the 2B5M treatment fall by over fifteen tokens (or about 20%) per unit sold. This decline will boost the earnings of buyers, and perhaps is the strongest indicator of monopsony power among the bargaining treatments.

Prices in other treatments (5M, 3M, and 2S5M) converge closer to the competitive prediction than to either Cournot or monopsony predictions. Price differences are significantly lower than the competitive norm, however, in the 5M and 3M treatments. We conclude that the Cournot model is not a good predictor of trades and prices where there is bilateral bargaining for price in the market environment created in this study, relative to the competitive and monopsony models. (9)

When the number of matches decreases for the buyer, as in the 2S5M case, the estimated price convergence level is not significantly different from that predicted by the competitive model. Nor is the price in this market environment significantly different from that in the 5M treatment. There is a contrast between buyer and seller concentration in these bargaining treatments. Compared to the 5M treatment, the concentration of buyers substantially decreases price, while the concentration of sellers does not generate a price increase. Although not conclusive from the experimental results reported here, the risk of holding inventory may work against the potential monopoly power of sellers. Still, prices in the 2S5M treatment generally are higher or not statistically different from levels in the other treatments, contributing to higher seller earnings.

Comparing average prices across bargaining rounds for periods sixteen to twenty (table 4), treatments containing five bargaining rounds (5M, 2B5M, 2S5M) all have a tendency toward higher prices in the first three rounds. The fourth round yields a modest price reduction. Prices are consistently lowest in the fifth bargaining round. Buyers are aware that sellers cannot hold over units and learn that sellers will accept lower bids to offset at least some production costs in the final round. These results suggest that in the last round sellers with unsold units are at the mercy of buyers in the market, even when there are two sellers. This appears to spill backward into earlier bargaining rounds particularly in the 3M and 2B5M treatments.

From the percent trades and average prices by round presented in table 4, there is support for the theoretical argument made earlier. That is, buyers and sellers have the incentive to trade early, diluting some of the buyers' bargaining power associated with advance production. In later rounds, the buyer has the advantage when matched with a seller having inventory in stock and facing the risk of losing the sunk unit production costs. When the matching problem is reduced for the buyers, as in the 2B5M treatment, they gain a bargaining advantage and monopsony power. Prices over all five bargaining rounds in this treatment are lower than in any other treatment. In the last bargaining round of this treatment, the price of 58.70 tokens is near the breakeven level for sellers, considering the average units traded are between three and four units for each seller.

We believe that the perception of price from the last round in the 3M treatment is more transparent for rounds one and two than in the 5M treatment, and prices in the 3M treatment are generally depressed below those in the 5M treatment. In the three-round treatment it is certainly more imperative to move the inventory, and at least a third is sold in each of the first two rounds. So, why do buyers trade during the early bargaining rounds in 5M, 3M, and 2B5M? Why not wait until the last rounds? It is because they never escape the matching problem and run the risk of losing gains from trade if in later bargaining rounds they are matched with a seller out of inventory.

Summary and Implications

Results of selected laboratory research reviewed and presented in this study are summarized in table 5. In general, auctions (double and English), with or without advance production, result in prices favorable to sellers, relative to other market environments. When there are many matches, as in a double auction, prices tend toward the competitive level. Reduced quantities traded, as compared to the competitive quantity, are consistently reported under each trading institution when there is advance production. This suggests a reduction in market efficiency, as measured by total surplus. Bilateral negotiation without advance production results in price near the competitive norm. Fewer trades, relative to the competitive level, have been reported for this trading institution. Increasing the number of matches in bilateral trading with advance production moves prices, although still lower, toward the competitive level. Sellers in a seller-concentrated market are able to negotiate for prices at the competitive norm. Advance production, combined with limited matches in private negotiation, can greatly disadvantage the bargaining position of sellers relative to buyers.

A lack of bargaining opportunities alone does not impact the bargaining advantage of one side of the market or the other in negotiating prices (Menkhaus et al. 2003). When sellers must produce in advance and have limited matches, the bargaining advantage and market power shifts to the buyer. The greater the matching problem faced by sellers in private negotiation markets with advance production, the greater the advantage to buyers. Further, advance production and the associated risk of inventory loss faced by producers of perishable products may keep buyers from losing bargaining power, even when there are fewer matches for them in a seller concentrated market.

It is not surprising that firms are eager to enter into vertical relations to avoid matching problems and sunk inventory costs. These arrangements are often beneficial to both buyers and sellers in reducing transaction costs. Nevertheless, the results of this study, given the parameters of the experiment, suggest the buyer has the advantage in specifying the terms of the vertical relations. Sellers who do not or cannot enter into vertical relations for private negotiation trading face matching and inventory loss risks. These sellers may, as a result, exchange commodities/products through other trading institutions such as auctions. Alternative institutions of exchange potentially could be thin or not exist, however, given that supplies for buyers are captive via vertical relations.

The results of experiments conducted in this study suggest that buyers in a concentrated market with private negotiation trading and advance production can exercise market power and extract monopsony rent. Prices are about 23% below the predicted competitive equilibrium and close to the monopsony price level. These lower prices are the result of tacit coordination enjoyed by buyers resulting from limited access and potential inventory loss from advance production faced by sellers, rather than collusive activities. The seller in a seller concentrated market is not as successful in extracting monopoly rent, although the price level is higher than when seller access is increased. Sellers can benefit by creating alliances or cooperatives to increase their bargaining position for price and overcome poor access to buyers. Changes in communication technology, such as electronic markets, can improve matches for both buyers and sellers.

These results provide evidence that can be useful to researchers investigating agent behavior in markets said to be concentrated and dominated by private negotiation. One such example, as identified above, is the issue of captive supplies in the fed cattle markets. Moreover, study results may provide a basis for evaluating potential regulations aimed at addressing alleged market power issues in commodity markets. Two industry practices that can contribute to reduced matches available to agricultural producers are shifts to grid marketing and short trading windows. The trend toward grid marketing may have shifted bargaining power to buyers by reducing the number of matches. Also, producers have alleged that there is a short period of time, or window, during which trading of fed cattle occurs--reducing the number of possible matches. Increased market concentration alone may not necessarily result in the use of market power by firms purchasing agricultural commodities/products. At issue are factors or influences that potentially facilitate the use of monopsony power, such as matching risk.

Finally, we have provided buyers with a bargaining advantage, because inventory must be sold. It is possible that buyers of inputs, for example, can face similar risks, such as filling fixed plant capacities. In such cases, the bargaining advantage of the buyer would be dampened, relative to those found and reported in this study. We also recognize that firms can be buyers at one stage of the food supply chain and sellers at another level.

[Received June 2006; accepted March 2007.]

References

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(1) Supplementary Appendix A (Menkhaus et al. 2007) provides more detail of inventory loss risk when sellers produce in advance of sale.

(2) Additional description of matching risk is contained in supplementary Appendix A (Menkhaus et al. 2007).

(3) Hong and Plott (1982) conducted experiments where trading occurred via negotiation by telephone with chosen trading partners. They found that as the number of matching opportunities increased in bilateral trading, prices approached the predicted competitive equilibrium and quantities traded were slightly higher than the competitive level. Private negotiation with many bargaining rounds resembles the matching rich double auction when there is no advance production. The double auction is "matching rich" in that when a bid or offer is announced, it is immediately available to all agents in the market. As a result, market participants have no difficulty finding a trading partner.

(4) This is a version of Akerlof's (1970) lemons problem. In our case, units held late in the production cycle are the "poorer" quality and these units drive down the price of units sold earlier in the cycle.

(5) There is some empirical evidence that directly suggests this type of control. For example, the price effects of advance production in the case of California iceberg lettuce are reported by Sexton and Zhang (1996). They document a decline in spot lettuce prices related to greater advance production. Their model allows for imperfect competition among buyers. From this, they estimate the loss in seller bargaining power due to a larger sunk lettuce harvest. Sexton and Zhang argue the buyers have an advantage "when the sellers' asset is sunk and highly perishable" (p. 932).

(6) On the rare occasion, it was necessary to ask individuals who happened to be in the vicinity of the experiment location, whether or not they had participated in a previous experiment, to fill in for a no show. Otherwise, new recruits were used for each replication of each treatment. Individual influences were minimized by averaging the data across individuals and replications in the analysis.

(7) For completeness, the estimated [[GAMMA].sub.j] (the starting level coefficients) and estimated starting levels are presented in supplementary Appendix B (Menkhaus et al. 2007) for the trade and price equations for each base category.

(8) The Parks method of estimation requires an equal number of observations in the times series (trading periods) of each cross section (treatment). There are twenty observations for each of the four test treatments (3M, 5M, 2B5M, and 2S5M) and another twenty observations for the base treatment for a total of a hundred observations for each equation in each of the three base categories (competitive, Cournot, or monopsony).

(9) We estimated the convergence models (trades and prices) for the Cournot solution for two sellers. This model did not perform as well as the competitive and monopsony models.

Dale J. Menkhaus is professor in the Department of Agricultural and Applied Economics. Owen R. Phillips is professor in the Department of Economics and Finance. Christopher T. Bastian is assistant professor, and Lance B. Gittings is former graduate assistant in the Department of Agricultural and Applied Economics. Menkhaus, Phillips, and Bastian are at the University of Wyoming.

Funding support was provided by the U.S. Department of Agriculture under Agreement No. 00-35400-9126 and the Lowham Research Endowment. Any opinions, findings, conclusions, or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the funding agencies. Helpful comments from anonymous reviewers and Editor Paul V. Preckel are gratefully acknowledged. Any remaining errors are the authors'. Table 1. Experiment Design--Private Negotiation Trading with Advance Production, Buyer and Seller Numbers and Alternative Buyer/Seller Matches Treatment No. of No. of No. of Designation

Buyers Sellers Matches 1 4 4 5 5M 2 4 4 3 3M 3 2 4 5 2B5M 4 4 2 5 2S5M Table 2. Unit Buyer Redemption Values and Seller Costs (Tokens) Used in the Experiments

Redemption Cost

Value for for Unit Buyers Sellers 1 130 30 2 120 40 3 110 50 4 100 60 5 90 70 6 80 80 7 70 90 8 60 100 Table 3. Asymptote Coefficients (Standard Errors) and [Convergence Levels]--for Trades and Prices--Competitive, Cournot, and Monopsony Bases by Treatment Treatment Competitive Competitive Cournot Asymptotes Trades Prices Trades Predicted base 20 80 19.56 5M -2.72 * (a) -2.36 * (a) -2.26 * (a)

(0.29) (0.77) (0.29)

[17.28] [77.64] [17.30] 3M -5.39 * (b) -7.06 * (b) -4.95 * (b)

(0.20) (0.72) (0.20)

[14.61] [72.94] [14.61] 2B5M -7.26 * (c) -17.58 * (c) -6.82 * (c)

(0.16) (0.80) (0.16)

[12.74] [62.42] [12.74] 2S5M -6.77 * (c) -0.96 (a) -6.33 * (c)

(0.18) (1.24) (0.18)

[13.23] [79.04] [13.23] [R.sup.2] 0.99 0.99 0.99 Treatment Cournot Monopsony Monopsony Asymptotes Prices Trades Prices Predicted base 86.11 16 60 5M -8.62 * (a) 1.29 * (a) 17.50 * (a)

(0.77) (0.29) (0.77)

[77.49] [17.29] [77.50] 3M -13.24 * (b) -1.40 * (b) 12.87 * (b)

(0.00) (0.20) (0.72)

[72.87] [14.60] [72.87] 2B5M -23.82 * (c) -3.27 * (c) 2.30 * (c)

(0.80) (0.16) (0.80)

[62.29] [12.73] [62.30] 2S5M -7.41 * (a) -2.77 * (c) 18.71 * (a)

(1.24) (0.18) (1.24)

[78.70] [13.23] [78.71] [R.sup.2] 0.99 0.99 0.99 Note: Single asterisk (*) denotes estimated convergence level significantly different from the base value, [alpha] = 0.01. Note: (a, b, c, d)--same letter indicates no significant difference between estimated convergence levels in the respective equations. Different letters indicate a significant difference between estimated asymptotes, [alpha] = 0.01. Table 4. Average Percentage of Trades and Average Prices for Each Bargaining Round by Treatment--Periods 16-20

Round 1 Round 2 Round 3 Round 4 Round 5

Treatment 5M % trades 37.90 22.85 20.60 7.74 10.91 Ave. price 78.48 80.50 80.36 77.56 66.33

Treatment 3M % trades 38.45 35.55 26.01 -- -- Ave. price 76.65 74.68 70.45 -- --

Treatment 2B5M % trades 31.09 28.28 18.00 14.13 8.50 Ave. price 65.39 64.64 65.57 63.29 58.70

Treatment 2S5M % trades 26.75 24.68 16.94 16.50 15.13 Ave. price 80.85 80.30 84.78 79.55 67.33 Table 5. Summary of Selected Laboratory Results Reviewed and Presented in This Article No. of No. of Trading Advance Resulting Buyers Sellers Institution (a) Production Quantity (b) Many Many CEM No [Q.sup.comp] 4 4 DA(PMK) * No [Q.sup.comp] 4 4 DA(PMK) Yes [Q.sup.comp] 4 4 EA(MPB) Yes [less than or

equal to]

[Q.sup.comp] 4 4 PN(MPJY) No <[Q.sup.comp] 4 4 PN(MPJY,CS) Yes <[Q.sup.comp] 4 4 PN(CS) Yes <[Q.sup.comp] 2 4 PN(CS) Yes <[Q.sup.comp] 4 2 PN(CS) Yes <[Q.sup.comp] No. of Resulting Buyer/Seller Buyers Price (b) Matches Many [P.sup.comp] Many 4 [P.sup.comp] Many 4 >[P.sup.comp] Many 4 >[P.sup.comp] -- 4 [P.sup.comp] 3 4 <[P.sup.comp] 3 4 <[P.sup.comp] 5 2 <[P.sup.comp] 5 4 [P.sup.comp] 5 * Sources: The laboratory results presented here are only those from selected literature reviewed in this study, along with those from the current study. These include: PMK--Phillips, Menkhaus, and Krogmeier (2001); MPB-Menkhaus, Phillips, and Bastian (2003); MPJY-Menkhaus et al. (2003); and CS--Current Study. (a) CEM--Competitive Equilibrium Model; DA--Double Auction; EA--English Auction; PN--Private Negotiation. (b) [Q.sup.comp]--Competitive Quantity Traded; [P.sup.comp]--Competitive Price.