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sloping reaction functions may arise only when the cross effects are strong compared with the
profitability of the industry.
Hence, the structure of the problem makes several types of interaction plausible. Free
riding would be represented by downward-sloping best-response functions. Following the
language of Bulow, Geanakoplos, and Klemperer , QASs are “strategic substitutes.” If one
firm invests heavily in a QAS, it will be a weak competitor in the second stage. It then may be
worthwhile for the other processor to free ride on the consumer trust obtained by the other
firm’s investments. Though mathematically possible, it is hard to rationalize a situation in
which a processor would choose stringent levels of assurance, believing that its rival will put a
lax system in place. If the processor’s rival invests little in quality, the firm will face a tough
Cournot competitor for the few periods the market is expected to last, which acts as a double
incentive to implement less stringent QASs.
A more plausible and intuitively appealing scenario is that of QASs being “strategic
complements.” That is, reaction functions have an upward slope. When a processor’s rival puts
a lax QAS in place, the firm will find little incentive to invest in quality assurance. As the
processor’s rival increases the stringency of the QAS, the firm will have two types of
incentives to raise its own investments. First, the market will last longer. Second, quantity
competition will be milder, which increases per period margins and makes more stringent
systems worthwhile.
Now when the capacity of consumers to perceive quality increases, the direction of the
response in the levels of assurance is ambiguous. Following Dixit, we totally differentiate the
system of first-order conditions to get