The two oligopolistic models cited most frequently are Bertrand and Cournot. In the Bertrand model, producers simultaneously and independently choose prices. Demand is allocated to the lower-price seller who then produces the quantity demanded at the stated price. Bertrand showed that the only equilibrium must be at the price that equals (constant) marginal cost. The Bertrand model was modified in the 1920s to introduce the possibility of limited capacity. Included was a set of demand and cost conditions postulating that one firm cannot serve the entire market. The implication is that, in such a situation, prices may be expected to fluctuate over a range, the upper and lower bounds of which depend on the respective capacities of competing companies. A further implication is that the market will tend to be unstable market while alternating between a price war phase and a price relaxing phase. The price path manifested by this model is referred to as a cycle.
Most recent studies of Bertrand oligopolies use one of two rationing rule assumptions. The rationing rule specifies the order in which buyers whose reservation values represent the demand curve are allowed to purchase one or more units. One rationing rule, value queue, allocates demand by moving down the demand curve. Under the value
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