4. Find a Nash equilibrium of a first-price sealed-bid auction with IPV, $n > 2$ bidders, and
uniform prior in which player $i$ bids according to the following bidding function: $\beta_i(v) =$
$(1 - \frac{1}{n})v$. Hint: Assuming that $\beta_i(v) = kv$, bidder 1's objective function becomes
$\max_{b_1 \in [0, k]} Pr(b_1 > \max\{\beta(v_2), ..., \beta(v_n)\})(v_1 - b_1)$.