Imitation in location choice

retail sites in a particular city for a fixed price. Similarly, marketing studies priced
proportionally to sample size, holding the list of predictors fixed, would not provide
purchasers of these services control over R² . Another example is the decision to spend
in-house research time analyzing Census data, which could lead to different model
specifications with distinct R² , but not continuous control over R² , since the list of
Census variables is exogenously fixed.

To investigate the consequences of discretizing the information acquisition deci-
sion, this section considers an information market in which both firms make a binary
decision of whether to acquire a privately available signal with fixed precision θ, at
cost c(θ^)2/2. Note that the error terms in the two firms’ private signals are inde-
pendent, although the signals themselves are of course correlated and the R² of each
are identical. This implies that, without the signal, Firm 1 faces expected costs of
deviating from a equal to σ_a². Acquiring the signal, Firm 1 faces expected costs of
deviating from a equal to σ2(1 — θ). Thus, Firm 1’s reduction in variance (i.e., in-
crease in expected profit owing to decreased expected deviation from a), achieved as
a result of acquiring the signal, equals σa0. Firm 1 acquires the signal if and only if:

c(0)²/2 < σ∖θ, or θ < 2σ^/c.                         (31)

If Firm 1 acquires the signal but Firm 2 does not, then Firm 2 faces expected
costs of deviating from a equal to σ2(1 — 0). If both firms acquire private signals,
then Firm 2’s expected cost of deviating from a equals σ2(1 — θ)/(1 + 0). Thus, Firm
2’s increase in expected profit by acquiring the signal is σ20(1 — θ)/(1 + θ), and it
decides to acquire the signal if and only if:

c(θɔ²/2 <σ²a0(1 — θ)/(1 + 0), or 0(1 + θ)/(1 — θ) < 2<%/c.        (32)

Figure 3 shows all possible discrete-information-acquisition environments indexed
by two exogenous parameters: the cost of deviating from the ideal location a rel-

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