31
9 For strategic substitutes, the optimal adjustment will depend not only on the sign of the cross
partial studied below, but also on the relative magnitude of a1,1 and a1,2 . To see this, impose
ds1* 1 ∂2E ∏1
symmetry and rewrite —- = —( - a 2 2 + α12 )------
dω Ω2,2 1,2 ∂s1∂ω
10 Note that the case where reputations is a public good, is also a Markov process, but with
only two possible states (corresponding to the first and fourth states of the current setting).
11 es
1 An example would be λ( s ) = —;—^
12 However, as Hennessy, Roosen, and Jensen note, branding also provides a target to
consumers in the marketplace when a problem occurs (more on this to follow).
13 A figure illustrating this point is available from the authors upon request.
14 Though not presented, as the demand for high quality products, (parameterized by a ) rises,
the stringency of the QAS under all scenarios increases.
15 A necessary condition for consumers to weakly prefer the monopoly situation over the
duopoly with public reputations is β(16mM - 9mD2 ) ≥ 7 , where mj , j= M,D represents the
equilibrium probabilities that reputations are maintained in two successive periods by the
monopolist and a duopolist respectively. A sufficient (not necessary) condition, is given by
βmD(16-9mD)≥7 , which is much harder to satisfy.
16 Note that if consumers value the future more than producers, or beta is close to 1 (higher
than 0.98), the expected utility from the monopoly scenario exceeds that of the duopoly with
public reputations for all ω . In those cases, the monopoly scenario would also Pareto
dominate the duopoly with public reputations.