9. (8%) Firms A, B, and C consider investments in research. Let $g_A$, $g_B$, and $g_C$ represent the amounts of research invested by A, B, and C, respectively. Given the investment $g_A$, $g_B$, and $g_C$, firm A's profit is

\[ \pi_A = 5 \ln(g_A + g_B + 1) - g_A; \] Firm B's is \[ \pi_B = 5 \ln(g_A + g_B + g_C + 1) - g_B; \] Firm C's is \[ \pi_C = 5 \ln(g_B + g_C + 1) - g_C. \]
The social welfare is defined to be $\pi_A + \pi_B + \pi_C$.
Which of the following statements is (are) correct?
(A) There is no Nash equilibrium.
(B) There are multiple Nash equilibria.
(C) There is a Nash equilibrium, which is socially optimal.
(D) All Nash equilibria are socially optimal.
(E) None of the above.

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