Q13: Compute the patent thicket of a firm.

There is a recent rise in interest in using unstructured data to boost trading and inform investment decisions. In this problem, we look at the asset pricing implication of patenting activities of a firm. We want to test whether the patent thicket of a firm has any predictive power for future firm value.

Patent thicket measure the degree of overlapting patent rights, which makes it harder for a new innovator to develop new technologies due to the complexity in licensing deals for multiple patents from multiple sources.

Patent thicket is also a mechanism used by firms to defend against competitiors and newcomers. One way to define patent thicket is to identify firm-groups that cite each other.

In the example above, A, B, C, D, E, F, G, H are firms. The arrows represent citations. For example, G cites H, but H does not cites G.

We can see that the firm-group {A, B, C} cites each other: A cites B and C, B cites A and C, and C cites A and B. {C, B, F} also cite each other.

The number of firm-groups that cite each other, such as {A, B, C}, is a measure for patent thicket (for the firms A, B, and C).

The above firms and their patent citation relationship can be represented as a array as follows:

# A, B, C, D, E, F, G, H

# A[0, 1, 1, 0, 0, 0, 0, 0]

# B[1, 0, 1, 0, 0, 1, 0, 0]

# C[1, 1, 0, 0, 0, 1, 0, 0]

# D[0, 0, 0, 0, 1, 0, 0, 0]

# E[0, 0, 0, 1, 0, 0, 0, 0]

# F[0, 1, 1, 0, 0, 0, 0, 0]

# G[0, 0, 0, 0, 0, 0, 0, 0]

# H[0, 0, 0, 0, 0, 0, 0, 0]

# For example A and B cite each other, hence the value 1 at location [A, B] and [B, A]

# For example C and F cite each other, hence the value 1 at location [C, F] and [F, C]

citation_list = [[0, 1, 1, 0, 0, 0, 0, 0],

[1, 0, 1, 0, 0, 1, 0, 0],

[1, 1, 0, 0, 0, 1, 0, 0],

[0, 0, 0, 0, 1, 0, 0, 0],

[0, 0, 0, 1, 0, 0, 0, 0],

[0, 1, 1, 0, 0, 0, 0, 0],

[0, 0, 0, 0, 0, 0, 0, 0],

[0, 0, 0, 0, 0, 0, 0, 0]]

citation_list

We convert this to an array.

citation_array = np.array(citation_list)

citation_array

Problem: Compute the number of thickets each firm A, B, C, D, E, F, G, H is in.