The Exercise of Seller Market Power without Explicit Collusion

One of the major factors considered in the antitrust analysis of mergers between firms in the same market is the possibility that a merged firm may be able to raise price, to the detriment of buyers. Of course, any seller may raise a price unilaterally, and so the real issue is the extent to which price can be raised profitably.

Such a price increase is more likely to raise profits if others in the market are not in a position to absorb increases in sales at lower prices, so the capacities of other sellers may constrain a firm’s market power, and a merger that reduces others’

capacities may create market power.

Even if a firm loses some sales as a result of a price increase, this may not be very detrimental to the firm’s profit if these “marginal” units are low-profit units, i.e.

if the costs of these units are close to the initial price. For example, consider the supply and demand structure on the left side of Figure 15.3. The supply function has a flat spot at a price of $2.60, where it crosses demand, and this competitive price is indicated by the thin horizontal line below the dots that represent transactions prices for the first 4 rounds of trading, which was done with posted-offer rules. The failure of price to converge to the competitive prediction was due to the fact that two

of the sellers had a number of units with costs at $2.60, so they had little incentive to cut price and sell these units, especially at prices just above this level. The narrow (1 unit) gap between demand and supply at prices just above the competitive level means that a seller who refuses to sell 2 of these low-profit marginal units would shift supply to the left by 2 units and raise the supply/demand intersection to the next highest supply step, at $2.80.

Figure 15.3 A Posted-Price Market with Seller Market Power

To summarize, market power to raise price above competitive levels can exist when competitors’ capacities are limited, and when a firm’s marginal units are selling at low per-unit profits. In addition, market power can be influenced by the nature of the trading institution. Vernon Smith (1981) investigated an extreme case of market power, with a single seller, and found that even monopolists in a double auction are sometimes not able to raise prices above competitive levels, whereas posted-offer monopolists are typically able to find and enforce monopoly price levels. The difference is that a seller in a posted offer auction sets a single, take-it-or-leave-it price, so sellers are not tempted to cut

cause prices in a double auction monopoly to be lower than the monopoly prediction.

This effect of the trading institution is also apparent from experiments conducted by Holt, Langan, and Villamil (1986) with the design from Figure 15.3, using 5 sellers and 5 buyers. As noted above, two of the sellers had higher capacities that included a number of low-profit units with costs at the competitive level of $2.60. In contrast, the large vertical difference between demand and the competitive price for all “included” units means that buyers had a strong incentive to buy these high-value units, even if price were increased above competitive levels. Thus the design was intended to create an asymmetry between buyers who were eager to buy, and sellers with little incentive to sell units at the margin, and hence with a large incentive to try to raise prices above competitive levels.

Despite this asymmetry, prices converged to competitive levels in about half of the sessions. Some modest price increases above competitive levels were observed in the other sessions, indicating that sellers could sometimes exercise market power even in a double auction.

Davis and Williams (1991) replicated the Holt, Langan, and Villamil results for double auctions with the market power design in Figure 15.3, and the resulting prices were slightly above competitive levels. In addition, they ran a new series of sessions using posted-offer trading, which generated somewhat higher price sequences like those observed in the figure.

Supra-competitive prices in posted-offer markets are not surprising, since experimental economists have long known that prices in posted-offer auctions tend to converge to competitive levels from above, if at all. This raises the question of whether these high prices can be explained by game-theoretic calculations. It is straightforward to specify a game-theoretic definition of market power, based on the incentive of one seller to raise price above a common competitive level (Holt, 1989). In other words, market power is said to exist when the competitive equilibrium is not a Nash equilibrium.

Although it is typically easy to check for the profitability of a unilateral deviation from a competitive outcome, it may be more difficult to identify the Nash equilibrium for a market with posted prices. The easiest case is where firms do not have constraints on what they can produce, a case commonly referred to as Bertrand competition. For example, if each firm has a common, constant marginal cost of C, then no common price above C would be a Nash equilibrium, since each firm would have an incentive to cut price slightly and capture all market sales. The Bertrand prediction for a price competition game played once is for a very harsh type of competition that drives price to marginal cost levels, even with only two or three firms.

Even with a repeated series of market periods, the one-shot Nash predictions may be relevant if random matchings are used to make the market

interactions have a one-shot nature, where nobody can punish or reward other’s pricing decisions in subsequent periods. Most market interactions are repeated, but if the number of market periods is fixed and known, then the one-shot Nash prediction applies in the final period, and a process of backward induction can be used to argue that prices in all periods would equal this one-shot Nash prediction.

In most markets, however, there is no well-defined final period, and in this case, there is a possibility that a kind of tacit cooperation might develop. In particular, a seller’s price restraint in one period might send a message that causes others to follow suite in subsequent periods, and sellers’ price cuts might be deterred by the threat of retaliatory price cuts by others. There are many ways that such tacit cooperation might develop, as supported by punishment and reward strategies, and the multiplicity of possible arrangements typically makes a theoretical analysis impossible without strong simplifying assumptions. Here is where experiments can help.

Figure 15.4 shows the results of a session with posted prices in which participants were matched in groups of 3, with no capacity constraints. Demand was simulated, with aggregate quantity being determined by the function, Q = 12 – P. In the first 10 rounds, all sellers had a constant marginal cost of $1, so the Bertrand prediction is $1. The 3-person groups were fixed, and this is probably a factor in the ability of sellers in one of the six triopoly groups to maintain prices at about $9, well above the Bertrand prediction. The price dots in the figure represent averages over all 3-person groups for each period, and these averages mask the fact that the 5 other triopoly groups were pricing much nearer to the Bertrand prediction of $1. The marginal cost was reduced to $0 for the final 10 periods, and matchings were reconfigured randomly after each period for this second treatment. The random matching is probably a factor in the somewhat sharper convergence of average prices to the Bertrand prediction in the final periods.

To summarize, we have identified several factors that may facilitate pricing at supra-competitive levels: 1) the price fixity and asymmetry of the posted-offer institution, relative to the double auction, 2) the extent to which market interactions are repeated, and 3) the structure of the seller costs and capacities, which may enable one seller to raise price without losing significant sales to others. The next section expands on the third factor, by providing a more detailed analysis of price competition with capacity constraints.

Figure 15.4. A Posted-Price Market with No Capacity Constraints and No Market Power