Dynamic Price Competition with Capacity Constraints and a Strategic Buyer

We analyze a simple dynamic durable good oligopoly model where sellers are capacity constrained. Two incumbent sellers and potential entrants choose their capacities at the start of the game. We solve for equilibrium capacity choices and the (necessarily mixed) pricing strategies. In equilibrium, the buyer splits the order with positive probability to preserve competition; thus it is possible that a high and low price seller both have sales. Sellers command a rent above the value of unmet demand by the other seller. A buyer would benet from either a commitment not to buy in the future or by hiring an agent with instructions to buy always from the lowest priced seller.