x
3
= 1, ω
i
= −1, π
i
= 0.5, ρ
i
= 0.5, and δ = 0.9, although similar figures could be generated
with alternative values. Here we set ω
1
= 5, ω
3
= 4, and k
1
= 0, and vary the number of
experimenters with policy 3 (k
3
). At the bottom of the figure, where k
3
= 0, the equilibrium
is the same as in the decision-theoretic case, illustrated near the top of Figure 3. With the
large value from the effective policies, both policies 1 and 3 are attractive as experimental
options, and therefore no policymaker would find policy 2 more beneficial in the first period.
[Figure 7 here.]
As the number of experimenters with policy 3 increases (moving upward on the figure),
experimentation with policy 3 becomes less attractive, with each additional experimenter
adding a smaller probability of being crucial to the discovery of the valence type. This is
indicated by the rightward movement of e
13
in Figure 7. For k
3
sufficiently large, e
k
1
12
≤ e
k
3
23
,
and we move from Case 2 of the game-theoretic model to Case 1. Here, because others
are experimenting with policy 3, where z
j
∈ e
k
1
12
, e
k
3
23
, S
j
will free-ride on the information
provided by others and adopt policy 2 in the first period. In some respects, this free-riding
behavior may be interpreted as induced policy moderation.
As per Lemma 1, further increases in k
3
move e
k
3
23
to the right, toward c
23
. Interestingly,
those increases also move e
k
1
12
to the left, affecting the first-period choice between policies
1 and 2. The intuition is as follows. With more policy 3 experimenters, the probability of
discovering that policy 3 is effective (θ
3
= θ) increases. Since adopting an effective policy
3 is the preferred alternative upon not uncovering an effective policy 1, the added value
of experimenting with policy 1 is diminished. Since the cost of experimenting is still the
same—forgoing a higher first-period expected utility—the range of free-riders is extended.
The interesting addition here beyond Lemma 1 is that these individuals are not free-riding
in the sense of having others carry out the experiment that they themselves would have
done (adopting policy 1). Rather, they free-ride on those who are experimenting with their
second-best policy choice.
5. Empirical Implications
One of our major motivating concerns in formulating this model was whether scholars
have been looking in the right places for evidence of learning and policy diffusion. Put simply,
would we observe the same behavior in a decision-theoretic model with no communication
across jurisdictions as in a game-theoretic model with learning externalities? And, have
19
Convention