Procurement Bidding with Restrictions

In many procurement situations with simultaneously offered projects, firms face participation restrictions and can bid only on a subset of the projects. This phenomenon is prevalent in a variety of observed situations such as bidding for private label supplies, business to business procurement or government projects. We show that for the case of n bidding firms where each is restricted to bid on a subset of the offered projects, there exists a symmetric equilibrium in which each bidder has a positive expected equilibrium profit. Prices are bounded away from marginal costs even if all the bidders are homogenous. this results from the fact that there is a positive probability that each firm will find itself in the position of being the sole bidder on a project. While the equilibrium probability of bidding on a project increases with its value, it is interesting to note that the bidding probability on the projects approaches an equiprobable one as the number of bidding firms increases. We find that the equilibrium profits decrease as firms are able to bid on more of the available projects. In contrast, bidder commitment to bid on specific projects increases the equilibrium profits of all firms. We also examine the effect of heterogeneity on equilibrium profits. Greater heterogeneity in the project valuations leads to lower firm profits. On the other hand, heterogeneity among bidders in terms of the number of projects that they are constrained to bid on leads to greater profits for the firms that can bid on more projects (regardless of the mix of the firms in the industry.) Finally, we analyze the effect of uncertainty in project valuations and show greater uncertainty in project valuations (as represented by a mean preserving spread) decreases the equilibrium profits. We conclude with an empirical analysis of bidding behavior that tests the predictions of the theory. We find that the probability of bidding on a particular project is increasing in its value, decreasing in the other projects values and decreasing in the number of bidding subjects. Furthermore, the value of the bids on a project increase with its valuation and decrease with the total number of bidders.