Conflicts of Interest during Contact Investigations: A Game-Theoretic Analysis

Table 1

Reduction in infection for Charlie due to disclosures by Charlie, assuming given strategies for the other two individuals. For each row, Alice is assumed to disclose either Bob or Charlie or both, as indicated in the first two columns; Bob is assumed to disclose either Alice or Charlie or both, as given in the next two columns. The next column (Alice versus none) shows how much the infection probability for Charlie is reduced by disclosing Alice instead of disclosing no one. The column labeled “Bob versus none” shows the reduction by disclosing Bob instead of no one and so forth. Analytic expressions for the quantities 𝐾₁, 𝐾₂, 𝐾₃, and 𝐾₄ are given in the text.

Alice; discloses		Bob; discloses		Reduction in infection probability for Charlie comparing disclosure choices of
Bob	Charlie	Alice	Charlie	Alice versus none	Bob versus none	Both versus none	Both versus Alice	Both versus Bob
N	N	N	N	0	0	0	0	0
Y	N	N	N	0	0	0	0	0
N	Y	N	N	0	𝐾2	𝐾2	𝐾2	0
Y	Y	N	N	0	𝐾4	𝐾4	𝐾4	0
N	N	Y	N	0	0	0	0	0
Y	N	Y	N	0	0	0	0	0
N	Y	Y	N	0	𝐾2	𝐾2	𝐾2	0
Y	Y	Y	N	0	𝐾4	𝐾4	𝐾4	0
N	N	N	Y	𝐾1	0	𝐾1	0	𝐾1
Y	N	N	Y	𝐾1	0	𝐾1	0	𝐾1
N	Y	N	Y	𝐾1	𝐾2	𝐾2+𝐾1	𝐾2	𝐾1
Y	Y	N	Y	𝐾1	𝐾4	𝐾4+𝐾1	𝐾4	𝐾1
N	N	Y	Y	𝐾3	0	𝐾3	0	𝐾3
Y	N	Y	Y	𝐾3	0	𝐾3	0	𝐾3
N	Y	Y	Y	𝐾3	𝐾2	𝐾2+𝐾3	𝐾2	𝐾3
Y	Y	Y	Y	𝐾3	𝐾4	𝐾4+𝐾3	𝐾4	𝐾3