Hedging feedback and pinning

Use the model of Proposition 9A.4. Nifty is at 22,750 with IV 12% and the 22,750 strike carries options on which dealers are net long 50 lakh units. Price impact is $\lambda=10^{-5}$ index points per unit of net futures flow. (a) Compute the ATM gamma per unit, the dealers' aggregate gamma $G$, $\lambda G$ and the damping factor $1/(1+\lambda G)$ with 2 hours and with 30 minutes to expiry (use $\tau$ = hours/8,760). (b) Repeat for dealers net short 50 lakh units. What happens as $\lambda|G|\to1$? (c) Prove Proposition 9A.4 and explain why the sign of dealer gamma cannot be read from the participant-wise OI file.