Resale Price Maintenance with Strategic Customers

We consider a decentralized supply chain (DSC) under resale price maintenance (RPM)selling a limited-lifetime product to forward-looking customers with heterogeneous valuations. When customers do not know the inventory level, double marginalization in DSC leads to a higher profit and lower aggregate welfare than in centralized supply chain (CSC). When customers know the inventory, DSC coincides with CSC. Thus, overestimation of customer awareness may lead to overcentralization of supply chains with profit loss comparable with the loss from strategic customers. The case with unknown inventory is extended to an arbitrary number of retailers with inventory-independent and inventory-dependent demand. In both cases, the manufacturer, by setting a higher wholesale price, mitigates the inventory-increasing effect of competition and reaches the same profit as with a single retailer. The high viability of RPM as a strategic-behavior-mitigating tool may serve as another explanation of why manufacturers may prefer DSC with RPM to a vertically integrated firm

Quantity Competition in the Presence of Strategic Consumers

Oligopolistic retailers decide on the initial inventories of an undifferentiated limited-lifetime product offered to strategic consumers. A manufacturer sets the first-period (full) price, while the second-period (clearance) price is determined by a market clearing process. The resulting symmetric pure-strategy equilibria may lead to no sales in the first or second period (Cournot outcome versus collusion), and sales in both periods with the clearance price above or at the salvage value. The equilibria possess a comprehensive set of monotonic properties. In particular, increasing strategic behavior can benefit retailers and hurt consumers, increasing competition may harm the local economy, and high levels of strategic behavior may insure against oversupply that leads to clearance sales at the salvage value. The welfare-optimal number of retailers can lead to the above-cost clearance price

Quantity Competition in the Presence of Strategic Consumers

Oligopolistic retailers decide on the initial inventories of an undifferentiated limited-lifetime product offered to strategic consumers. A manufacturer sets the first-period (full) price, while the second-period (clearance) price is determined by a market clearing process. The resulting symmetric pure-strategy equilibria may lead to no sales in the first or second period (Cournot outcome versus collusion), and sales in both periods with the clearance price above or at the salvage value. The equilibria possess a comprehensive set of monotonic properties. In particular, increasing strategic behavior can benefit retailers and hurt consumers, increasing competition may harm the local economy, and high levels of strategic behavior may insure against oversupply that leads to clearance sales at the salvage value. The welfare-optimal number of retailers can lead to the above-cost clearance price

Resale Price Maintenance with Strategic Customers

We consider a decentralized supply chain (DSC) under resale price maintenance (RPM)selling a limited-lifetime product to forward-looking customers with heterogeneous valuations. When customers do not know the inventory level, double marginalization in DSC leads to a higher profit and lower aggregate welfare than in centralized supply chain (CSC). When customers know the inventory, DSC coincides with CSC. Thus, overestimation of customer awareness may lead to overcentralization of supply chains with profit loss comparable with the loss from strategic customers. The case with unknown inventory is extended to an arbitrary number of retailers with inventory-independent and inventory-dependent demand. In both cases, the manufacturer, by setting a higher wholesale price, mitigates the inventory-increasing effect of competition and reaches the same profit as with a single retailer. The high viability of RPM as a strategic-behavior-mitigating tool may serve as another explanation of why manufacturers may prefer DSC with RPM to a vertically integrated firm

Quantity Competition under Resale Price Maintenance when Most Favored Customers are Strategic

Legal studies usually treat a policy of a manufacturer or retailer as socially harmful if it reduces product output and increases the price. We consider a two-period model where the first-period price is fixed by resale price maintenance (RPM) and resellers endogenously decide to use another "collusion suspect," meet-the-competition clause with a most-favored-customer clause (MFC), to counteract strategic customer behavior. As a result of MFC, second-period (reduced) price increases, and resellers' inventories decrease. However, customer surplus may increase and aggregate welfare increases in the majority of market situations. MFC can not only decrease the losses in welfare and resellers' profits due to strategic customers but, under reseller competition, may even lead to higher levels of these values than with myopic customers, i.e., to gains from increased strategic behavior. MFC may create "MFC-traps" for resellers, where one of possible market outcomes yields a gain from increased strategic behavior while another results in a reseller profit less than the worst profit in any stable outcome without MFC. With growing competition, benefits or losses from MFC can be higher than losses from strategic customer behavior

Fréchet optimal bounds on the probability of a union with supplementary information

We show that bounds for the probability of a union involving either lower order binomial moments or lower order probabilities of events may be considerably improved in the presence of supplementary information such as a bound on the number of events that can occur simultaneously or bounds on their probabilities. An example shows how such additional information often may be provided naturally. We also prove the Fréchet optimality of these bounds using linear programming.Boole's inequality Degree one Fréchet optimal Linear programming Probability bound Supplementary information