with Lauren Xiaoyuan Lu
Abstract
We consider a supply chain in which a supplier sells
products to multiple retailers. When orders from the retailers exceed the
supplier's capacity, she must employ an allocation mechanism to balance supply
and demand. In particular, we consider a commonly used allocation scheme in the
automobile industry: turn-and-earn, which uses past sales to allocate capacity.
In essence, dealers "earn" allotment of a vehicle after they sell
one. In contrast to turn-and-earn, fixed allocation ignores past sales and
gives retailers equal share of the capacity. Earlier work has demonstrated that
turn-and-earn induces more sales in a two-period setting compared to fixed
allocation. The question remains unanswered whether turn-and-earn induces
similar behaviors over a long horizon when retailers possess private demand
information. We construct a dynamic stochastic game of order competition over
an infinite horizon to track the order dynamics of the supply chain. We obtain
a richer set of equilibrium behaviors than existing models predict. Instead of
a symmetric allocation outcome, we observe that sales leadership may arise in
equilibrium and that retailers with different past sales adopt distinct
ordering strategies to respond to demand uncertainty. Transient sales dynamics
suggest that sales leadership may not be persistent and can be eliminated by
the occurrence of extremely low demand. This provides a theoretical explanation
for several behavioral observations of some